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Título : Handbook of K-Theory Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Eric M. Friedlander ; Daniel R. Grayson Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Número de páginas: eReference Il.: online resource ISBN/ISSN/DL: 978-3-540-27855-9 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry K-theory Number theory topology K-Theory Geometry Topology Theory Clasificación: 51 Matemáticas Resumen: This handbook offers a compilation of techniques and results in K-theory. These two volumes consist of chapters, each of which is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. The overall intent of this handbook is to offer the interested reader an exposition of our current state of knowledge as well as an implicit blueprint for future research. This handbook should be especially useful for students wishing to obtain an overview of K-theory and for mathematicians interested in pursuing challenges in this rapidly expanding field Nota de contenido: Part I: Foundations and Computations: Deloopings in Algebraic K- theory -- The Motivic Spectral Sequence -- K-theory of truncated polynomial algebras -- Bott Periodicity in Topological, Algebraic and Hermitian K-theory -- Algebraic K-theory of Rings and Integers in Local and Global Fields. Part II: K-theory and Algebraic Geometry: Motivic Cohomology, K-theory and topological cyclic Homology -- K-theory and Intersection Theory -- Regulators -- Algebraic K-theory, Algebraic Cycles and Arithmetic Geometry -- Mixed Motives. Part III: K-theory and Geometric Topology: Witt Groups -- K-theory and Geometric Topology -- Quadratic K-theory and Geometric Topology. Part IV: K-theory and Operator Algebras: Bivariant K-and Cyclic Theories -- The Baum-Connes and the Farrell-Jones Conjectures in K-and L-theory -- Comparison Between Algebraic and Topological K-theory for Banach Algebras and C*-Algebras. Part V: Other Forms of K-theory: Semi-topological K-theory -- Equivariant K-theory -- K(1)-local Homotopy Theory, Iwasawa Theory and Algebraic K-theory -- The K-theory of Triangulated Categories En línea: http://dx.doi.org/10.1007/978-3-540-27855-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35287 Handbook of K-Theory [documento electrónico] / SpringerLink (Online service) ; Eric M. Friedlander ; Daniel R. Grayson . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2005 . - eReference : online resource.
ISBN : 978-3-540-27855-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry K-theory Number theory topology K-Theory Geometry Topology Theory Clasificación: 51 Matemáticas Resumen: This handbook offers a compilation of techniques and results in K-theory. These two volumes consist of chapters, each of which is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. The overall intent of this handbook is to offer the interested reader an exposition of our current state of knowledge as well as an implicit blueprint for future research. This handbook should be especially useful for students wishing to obtain an overview of K-theory and for mathematicians interested in pursuing challenges in this rapidly expanding field Nota de contenido: Part I: Foundations and Computations: Deloopings in Algebraic K- theory -- The Motivic Spectral Sequence -- K-theory of truncated polynomial algebras -- Bott Periodicity in Topological, Algebraic and Hermitian K-theory -- Algebraic K-theory of Rings and Integers in Local and Global Fields. Part II: K-theory and Algebraic Geometry: Motivic Cohomology, K-theory and topological cyclic Homology -- K-theory and Intersection Theory -- Regulators -- Algebraic K-theory, Algebraic Cycles and Arithmetic Geometry -- Mixed Motives. Part III: K-theory and Geometric Topology: Witt Groups -- K-theory and Geometric Topology -- Quadratic K-theory and Geometric Topology. Part IV: K-theory and Operator Algebras: Bivariant K-and Cyclic Theories -- The Baum-Connes and the Farrell-Jones Conjectures in K-and L-theory -- Comparison Between Algebraic and Topological K-theory for Banach Algebras and C*-Algebras. Part V: Other Forms of K-theory: Semi-topological K-theory -- Equivariant K-theory -- K(1)-local Homotopy Theory, Iwasawa Theory and Algebraic K-theory -- The K-theory of Triangulated Categories En línea: http://dx.doi.org/10.1007/978-3-540-27855-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35287 Ejemplares
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Título : Polytopes, Rings, and K-Theory Tipo de documento: documento electrónico Autores: Joseph Gubeladze ; SpringerLink (Online service) ; Winfried Bruns Editorial: New York, NY : Springer New York Fecha de publicación: 2009 Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XIV, 461 p. 52 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-76356-9 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Commutative algebra rings K-theory Convex geometry Discrete Rings and Algebras K-Theory Geometry Clasificación: 51 Matemáticas Resumen: This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, the algebras derived from them, and toric varieties. The book discusses several properties and invariants of these objects, such as efficient generation, unimodular triangulations and covers, basic theory of monoid rings, isomorphism problems and automorphism groups, homological properties and enumerative combinatorics. The last part is an extensive treatment of the K-theory of monoid rings, with extensions to toric varieties and their intersection theory. This monograph has been written with a view towards graduate students and researchers who want to study the cross-connections of algebra and discrete convex geometry. While the text has been written from an algebraist's view point, also specialists in lattice polytopes and related objects will find an up-to-date discussion of affine monoids and their combinatorial structure. Though the authors do not explicitly formulate algorithms, the book takes a constructive approach wherever possible. Winfried Bruns is Professor of Mathematics at Universität Osnabrück. Joseph Gubeladze is Professor of Mathematics at San Francisco State University Nota de contenido: I Cones, monoids, and triangulations -- Polytopes, cones, and complexes -- Affine monoids and their Hilbert bases -- Multiples of lattice polytopes -- II Affine monoid algebras -- Monoid algebras -- Isomorphisms and automorphisms -- Homological properties and Hilbert functions -- Gr#x00F6;bner bases, triangulations, and Koszul algebras -- III K-theory -- Projective modules over monoid rings -- Bass#x2013;Whitehead groups of monoid rings -- Varieties En línea: http://dx.doi.org/10.1007/b105283 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33863 Polytopes, Rings, and K-Theory [documento electrónico] / Joseph Gubeladze ; SpringerLink (Online service) ; Winfried Bruns . - New York, NY : Springer New York, 2009 . - XIV, 461 p. 52 illus : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-0-387-76356-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Commutative algebra rings K-theory Convex geometry Discrete Rings and Algebras K-Theory Geometry Clasificación: 51 Matemáticas Resumen: This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, the algebras derived from them, and toric varieties. The book discusses several properties and invariants of these objects, such as efficient generation, unimodular triangulations and covers, basic theory of monoid rings, isomorphism problems and automorphism groups, homological properties and enumerative combinatorics. The last part is an extensive treatment of the K-theory of monoid rings, with extensions to toric varieties and their intersection theory. This monograph has been written with a view towards graduate students and researchers who want to study the cross-connections of algebra and discrete convex geometry. While the text has been written from an algebraist's view point, also specialists in lattice polytopes and related objects will find an up-to-date discussion of affine monoids and their combinatorial structure. Though the authors do not explicitly formulate algorithms, the book takes a constructive approach wherever possible. Winfried Bruns is Professor of Mathematics at Universität Osnabrück. Joseph Gubeladze is Professor of Mathematics at San Francisco State University Nota de contenido: I Cones, monoids, and triangulations -- Polytopes, cones, and complexes -- Affine monoids and their Hilbert bases -- Multiples of lattice polytopes -- II Affine monoid algebras -- Monoid algebras -- Isomorphisms and automorphisms -- Homological properties and Hilbert functions -- Gr#x00F6;bner bases, triangulations, and Koszul algebras -- III K-theory -- Projective modules over monoid rings -- Bass#x2013;Whitehead groups of monoid rings -- Varieties En línea: http://dx.doi.org/10.1007/b105283 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33863 Ejemplares
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Título : The Local Structure of Algebraic K-Theory Tipo de documento: documento electrónico Autores: Bjørn Ian Dundas ; SpringerLink (Online service) ; Thomas G. Goodwillie ; Randy McCarthy Editorial: London : Springer London Fecha de publicación: 2012 Otro editor: Imprint: Springer Colección: Algebra and Applications, ISSN 1572-5553 num. 18 Número de páginas: XVI, 436 p Il.: online resource ISBN/ISSN/DL: 978-1-4471-4393-2 Idioma : Inglés (eng) Palabras clave: Mathematics Category theory (Mathematics) Homological algebra K-theory Algebraic topology K-Theory Topology Theory, Algebra Clasificación: 51 Matemáticas Resumen: Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology Nota de contenido: Algebraic K-theory -- Gamma-spaces and S-algebras -- Reductions -- Topological Hochschild Homology -- The Trace K ? THH -- Topological Cyclic Homology -- The Comparison of K-theory and TC En línea: http://dx.doi.org/10.1007/978-1-4471-4393-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32729 The Local Structure of Algebraic K-Theory [documento electrónico] / Bjørn Ian Dundas ; SpringerLink (Online service) ; Thomas G. Goodwillie ; Randy McCarthy . - London : Springer London : Imprint: Springer, 2012 . - XVI, 436 p : online resource. - (Algebra and Applications, ISSN 1572-5553; 18) .
ISBN : 978-1-4471-4393-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Category theory (Mathematics) Homological algebra K-theory Algebraic topology K-Theory Topology Theory, Algebra Clasificación: 51 Matemáticas Resumen: Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology Nota de contenido: Algebraic K-theory -- Gamma-spaces and S-algebras -- Reductions -- Topological Hochschild Homology -- The Trace K ? THH -- Topological Cyclic Homology -- The Comparison of K-theory and TC En línea: http://dx.doi.org/10.1007/978-1-4471-4393-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32729 Ejemplares
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Título : Topological and Bivariant K-Theory Tipo de documento: documento electrónico Autores: Joachim Cuntz ; SpringerLink (Online service) ; Ralf Meyer ; Jonathan M. Rosenberg Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2007 Colección: Oberwolfach Seminars num. 36 Número de páginas: XII, 262 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8399-2 Idioma : Inglés (eng) Palabras clave: Mathematics K-theory Topology K-Theory Clasificación: 51 Matemáticas Resumen: Topological K-theory is one of the most important invariants for noncommutative algebras equipped with a suitable topology or bornology. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. We describe a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, we discuss other approaches to bivariant K-theories for operator algebras. As applications, we study K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem Nota de contenido: The elementary algebra of K-theory -- Functional calculus and topological K-theory -- Homotopy invariance of stabilised algebraic K-theory -- Bott periodicity -- The K-theory of crossed products -- Towards bivariant K-theory: how to classify extensions -- Bivariant K-theory for bornological algebras -- A survey of bivariant K-theories -- Algebras of continuous trace, twisted K-theory -- Crossed products by ? and Connes’ Thom Isomorphism -- Applications to physics -- Some connections with index theory -- Localisation of triangulated categories En línea: http://dx.doi.org/10.1007/978-3-7643-8399-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34713 Topological and Bivariant K-Theory [documento electrónico] / Joachim Cuntz ; SpringerLink (Online service) ; Ralf Meyer ; Jonathan M. Rosenberg . - Basel : Birkhäuser Basel, 2007 . - XII, 262 p : online resource. - (Oberwolfach Seminars; 36) .
ISBN : 978-3-7643-8399-2
Idioma : Inglés (eng)
Palabras clave: Mathematics K-theory Topology K-Theory Clasificación: 51 Matemáticas Resumen: Topological K-theory is one of the most important invariants for noncommutative algebras equipped with a suitable topology or bornology. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. We describe a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, we discuss other approaches to bivariant K-theories for operator algebras. As applications, we study K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem Nota de contenido: The elementary algebra of K-theory -- Functional calculus and topological K-theory -- Homotopy invariance of stabilised algebraic K-theory -- Bott periodicity -- The K-theory of crossed products -- Towards bivariant K-theory: how to classify extensions -- Bivariant K-theory for bornological algebras -- A survey of bivariant K-theories -- Algebras of continuous trace, twisted K-theory -- Crossed products by ? and Connes’ Thom Isomorphism -- Applications to physics -- Some connections with index theory -- Localisation of triangulated categories En línea: http://dx.doi.org/10.1007/978-3-7643-8399-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34713 Ejemplares
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Título : Algebraic Cobordism Tipo de documento: documento electrónico Autores: Marc Levine ; SpringerLink (Online service) ; Fabien Morel Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2007 Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XII, 246 p Il.: online resource ISBN/ISSN/DL: 978-3-540-36824-3 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Commutative algebra rings K-theory Topology topology Geometry Rings and Algebras K-Theory Clasificación: 51 Matemáticas Resumen: Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen's theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over the Lazard ring by the elements of positive degrees. This implies in particular the generalized degree formula conjectured by Rost. The book also contains some examples of computations and applications Nota de contenido: Introduction -- I. Cobordism and oriented cohomology -- 1.1. Oriented cohomology theories. 1.2. Algebraic cobordism. 1.3. Relations with complex cobordism. - II. The definition of algebraic cobordism. 2.1. Oriented Borel-Moore functions. 2.2. Oriented functors of geometric type. 2.3. Some elementary properties. 2.4. The construction of algebraic cobordism. 2.5. Some computations in algebraic cobordism -- III. Fundamental properties of algebraic cobordism. 3.1. Divisor classes. 3.2. Localization. 3.3. Transversality. 3.4. Homotopy invariance. 3.5. The projective bundle formula. 3.6. The extended homotopy property. IV. Algebraic cobordism and the Lazard ring. 4.1. Weak homology and Chern classes. 4.2. Algebraic cobordism and K-theory. 4.3. The cobordism ring of a point. 4.4. Degree formulas. 4.5. Comparison with the Chow groups. V. Oriented Borel-Moore homology. 5.1. Oriented Borel-Moore homology theories. 5.2. Other oriented theories -- VI. Functoriality. 6.1. Refined cobordism. 6.2. Intersection with a pseudo-divisor. 6.3. Intersection with a pseudo-divisor II. 6.4. A moving lemma. 6.5. Pull-back for l.c.i. morphisms. 6.6. Refined pull-back and refined intersections. VII. The universality of algebraic cobordism. 7.1. Statement of results. 7.2. Pull-back in Borel-Moore homology theories. 7.3. Universality 7.4. Some applications -- Appendix A: Resolution of singularities -- References -- Index -- Glossary of Notation En línea: http://dx.doi.org/10.1007/3-540-36824-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34628 Algebraic Cobordism [documento electrónico] / Marc Levine ; SpringerLink (Online service) ; Fabien Morel . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2007 . - XII, 246 p : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-3-540-36824-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Commutative algebra rings K-theory Topology topology Geometry Rings and Algebras K-Theory Clasificación: 51 Matemáticas Resumen: Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen's theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over the Lazard ring by the elements of positive degrees. This implies in particular the generalized degree formula conjectured by Rost. The book also contains some examples of computations and applications Nota de contenido: Introduction -- I. Cobordism and oriented cohomology -- 1.1. Oriented cohomology theories. 1.2. Algebraic cobordism. 1.3. Relations with complex cobordism. - II. The definition of algebraic cobordism. 2.1. Oriented Borel-Moore functions. 2.2. Oriented functors of geometric type. 2.3. Some elementary properties. 2.4. The construction of algebraic cobordism. 2.5. Some computations in algebraic cobordism -- III. Fundamental properties of algebraic cobordism. 3.1. Divisor classes. 3.2. Localization. 3.3. Transversality. 3.4. Homotopy invariance. 3.5. The projective bundle formula. 3.6. The extended homotopy property. IV. Algebraic cobordism and the Lazard ring. 4.1. Weak homology and Chern classes. 4.2. Algebraic cobordism and K-theory. 4.3. The cobordism ring of a point. 4.4. Degree formulas. 4.5. Comparison with the Chow groups. V. Oriented Borel-Moore homology. 5.1. Oriented Borel-Moore homology theories. 5.2. Other oriented theories -- VI. Functoriality. 6.1. Refined cobordism. 6.2. Intersection with a pseudo-divisor. 6.3. Intersection with a pseudo-divisor II. 6.4. A moving lemma. 6.5. Pull-back for l.c.i. morphisms. 6.6. Refined pull-back and refined intersections. VII. The universality of algebraic cobordism. 7.1. Statement of results. 7.2. Pull-back in Borel-Moore homology theories. 7.3. Universality 7.4. Some applications -- Appendix A: Resolution of singularities -- References -- Index -- Glossary of Notation En línea: http://dx.doi.org/10.1007/3-540-36824-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34628 Ejemplares
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