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Título : Elliptic Curves, Hilbert Modular Forms and Galois Deformations Tipo de documento: documento electrónico Autores: Laurent Berger ; SpringerLink (Online service) ; Gebhard Böckle ; Lassina Dembélé ; Mladen Dimitrov ; Tim Dokchitser ; John Voight Editorial: Basel : Springer Basel Fecha de publicación: 2013 Otro editor: Imprint: Birkhäuser Colección: Advanced Courses in Mathematics - CRM Barcelona, ISSN 2297-0304 Número de páginas: XII, 249 p. 11 illus., 2 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-0348-0618-3 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Algebraic geometry Number theory Theory Geometry Clasificación: 51 Matemáticas Resumen: The notes in this volume correspond to advanced courses held at the Centre de Recerca Matemàtica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year. The notes by Laurent Berger provide an introduction to p-adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at p that arise naturally in Galois deformation theory. The notes by Gebhard Böckle offer a comprehensive course on Galois deformation theory, starting from the foundational results of Mazur and discussing in detail the theory of pseudo-representations and their deformations, local deformations at places l ? p and local deformations at p which are flat. In the last section,the results of Böckle and Kisin on presentations of global deformation rings over local ones are discussed. The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients. The notes by Lassina Dembélé and John Voight describe methods for performing explicit computations in spaces of Hilbert modular forms. These methods depend on the Jacquet-Langlands correspondence and on computations in spaces of quaternionic modular forms, both for the case of definite and indefinite quaternion algebras. Several examples are given, and applications to modularity of Galois representations are discussed. The notes by Tim Dokchitser describe the proof, obtained by the author in a joint project with Vladimir Dokchitser, of the parity conjecture for elliptic curves over number fields under the assumption of finiteness of the Tate-Shafarevich group. The statement of the Birch and Swinnerton-Dyer conjecture is included, as well as a detailed study of local and global root numbers of elliptic curves and their classification Nota de contenido: Part I: Galois Deformations -- On p-adic Galois Representations -- Deformations of Galois Representations -- Part II: Hilbert Modular Forms -- Arithmetic Aspects of Hilbert Modular Forms and Varieties -- Explicit Methods for Hilbert Modular Forms -- Part III: Elliptic Curves -- Notes on the Parity Conjecture En línea: http://dx.doi.org/10.1007/978-3-0348-0618-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32442 Elliptic Curves, Hilbert Modular Forms and Galois Deformations [documento electrónico] / Laurent Berger ; SpringerLink (Online service) ; Gebhard Böckle ; Lassina Dembélé ; Mladen Dimitrov ; Tim Dokchitser ; John Voight . - Basel : Springer Basel : Imprint: Birkhäuser, 2013 . - XII, 249 p. 11 illus., 2 illus. in color : online resource. - (Advanced Courses in Mathematics - CRM Barcelona, ISSN 2297-0304) .
ISBN : 978-3-0348-0618-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Algebraic geometry Number theory Theory Geometry Clasificación: 51 Matemáticas Resumen: The notes in this volume correspond to advanced courses held at the Centre de Recerca Matemàtica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year. The notes by Laurent Berger provide an introduction to p-adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at p that arise naturally in Galois deformation theory. The notes by Gebhard Böckle offer a comprehensive course on Galois deformation theory, starting from the foundational results of Mazur and discussing in detail the theory of pseudo-representations and their deformations, local deformations at places l ? p and local deformations at p which are flat. In the last section,the results of Böckle and Kisin on presentations of global deformation rings over local ones are discussed. The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients. The notes by Lassina Dembélé and John Voight describe methods for performing explicit computations in spaces of Hilbert modular forms. These methods depend on the Jacquet-Langlands correspondence and on computations in spaces of quaternionic modular forms, both for the case of definite and indefinite quaternion algebras. Several examples are given, and applications to modularity of Galois representations are discussed. The notes by Tim Dokchitser describe the proof, obtained by the author in a joint project with Vladimir Dokchitser, of the parity conjecture for elliptic curves over number fields under the assumption of finiteness of the Tate-Shafarevich group. The statement of the Birch and Swinnerton-Dyer conjecture is included, as well as a detailed study of local and global root numbers of elliptic curves and their classification Nota de contenido: Part I: Galois Deformations -- On p-adic Galois Representations -- Deformations of Galois Representations -- Part II: Hilbert Modular Forms -- Arithmetic Aspects of Hilbert Modular Forms and Varieties -- Explicit Methods for Hilbert Modular Forms -- Part III: Elliptic Curves -- Notes on the Parity Conjecture En línea: http://dx.doi.org/10.1007/978-3-0348-0618-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32442 Ejemplares
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Título : Modern Optimization Modelling Techniques Tipo de documento: documento electrónico Autores: Roberto Cominetti ; SpringerLink (Online service) ; Francisco Facchinei ; Jean-Bernard Lasserre Editorial: Basel : Springer Basel Fecha de publicación: 2012 Otro editor: Imprint: Birkhäuser Colección: Advanced Courses in Mathematics - CRM Barcelona, ISSN 2297-0304 Número de páginas: IX, 269 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0291-8 Idioma : Inglés (eng) Palabras clave: Mathematics Game theory Operations research Management science Research, Science Theory, Economics, Social and Behav. Sciences Clasificación: 51 Matemáticas Resumen: This book contains an expanded version of three series of lectures delivered by the authors at the CRM in July 2009. The theory of optimization, understood in a broad sense, is the basis of modern applied mathematics, covering a large spectrum of topics from theoretical considerations (structure, stability) to applied operational research and engineering applications. The compiled material of this book puts on display this versatility, by exhibiting the three parallel and complementary components of optimization: theory, algorithms, and practical problems. The first part is a self-contained course on the general moment problem and its relations with semidefinite programming. The second part is dedicated to the problem of determination of Nash equilibria from an algorithmic viewpoint. The last part presents congestion models for traffic networks and develops modern optimization techniques for finding traffic equilibria based on stochastic optimization and game theory Nota de contenido: Part I: Moments and Positive Polynomials for Optimization by Jean B. Lasserre -- Part II: Computation of Generalized Nash Equilibria: Recent Advancements by Francisco Facchinei -- Part III: Equilibrium and Learning in Traffic Networks by Roberto Cominetti En línea: http://dx.doi.org/10.1007/978-3-0348-0291-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32875 Modern Optimization Modelling Techniques [documento electrónico] / Roberto Cominetti ; SpringerLink (Online service) ; Francisco Facchinei ; Jean-Bernard Lasserre . - Basel : Springer Basel : Imprint: Birkhäuser, 2012 . - IX, 269 p : online resource. - (Advanced Courses in Mathematics - CRM Barcelona, ISSN 2297-0304) .
ISBN : 978-3-0348-0291-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Game theory Operations research Management science Research, Science Theory, Economics, Social and Behav. Sciences Clasificación: 51 Matemáticas Resumen: This book contains an expanded version of three series of lectures delivered by the authors at the CRM in July 2009. The theory of optimization, understood in a broad sense, is the basis of modern applied mathematics, covering a large spectrum of topics from theoretical considerations (structure, stability) to applied operational research and engineering applications. The compiled material of this book puts on display this versatility, by exhibiting the three parallel and complementary components of optimization: theory, algorithms, and practical problems. The first part is a self-contained course on the general moment problem and its relations with semidefinite programming. The second part is dedicated to the problem of determination of Nash equilibria from an algorithmic viewpoint. The last part presents congestion models for traffic networks and develops modern optimization techniques for finding traffic equilibria based on stochastic optimization and game theory Nota de contenido: Part I: Moments and Positive Polynomials for Optimization by Jean B. Lasserre -- Part II: Computation of Generalized Nash Equilibria: Recent Advancements by Francisco Facchinei -- Part III: Equilibrium and Learning in Traffic Networks by Roberto Cominetti En línea: http://dx.doi.org/10.1007/978-3-0348-0291-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32875 Ejemplares
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Título : Nonlinear Partial Differential Equations Tipo de documento: documento electrónico Autores: Luis A. Caffarelli ; SpringerLink (Online service) ; François Golse ; Yan Guo ; Carlos E. Kenig ; Alexis Vasseur Editorial: Basel : Springer Basel Fecha de publicación: 2012 Colección: Advanced Courses in Mathematics - CRM Barcelona, ISSN 2297-0304 Número de páginas: VIII, 150 p. 33 illus., 10 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-0348-0191-1 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Mathematical physics Differential Equations Physics Clasificación: 51 Matemáticas Resumen: The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrödinger and wave equations. Several powerful methods from recent top research articles are described in a careful and expository manner Nota de contenido: Foreword. 1 The De Giorgi Method for Nonlocal Fluid Dynamics -- 2 Recent Results on the Periodic Lorentz Gas -- 3 The Boltzmann Equation in Bounded Domains -- 4 The Concentration-Compactness/Rigidity Method for Critical Dispersive and Wave Equations En línea: http://dx.doi.org/10.1007/978-3-0348-0191-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32860 Nonlinear Partial Differential Equations [documento electrónico] / Luis A. Caffarelli ; SpringerLink (Online service) ; François Golse ; Yan Guo ; Carlos E. Kenig ; Alexis Vasseur . - Basel : Springer Basel, 2012 . - VIII, 150 p. 33 illus., 10 illus. in color : online resource. - (Advanced Courses in Mathematics - CRM Barcelona, ISSN 2297-0304) .
ISBN : 978-3-0348-0191-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Mathematical physics Differential Equations Physics Clasificación: 51 Matemáticas Resumen: The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrödinger and wave equations. Several powerful methods from recent top research articles are described in a careful and expository manner Nota de contenido: Foreword. 1 The De Giorgi Method for Nonlocal Fluid Dynamics -- 2 Recent Results on the Periodic Lorentz Gas -- 3 The Boltzmann Equation in Bounded Domains -- 4 The Concentration-Compactness/Rigidity Method for Critical Dispersive and Wave Equations En línea: http://dx.doi.org/10.1007/978-3-0348-0191-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32860 Ejemplares
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Título : Simplicial Methods for Operads and Algebraic Geometry Tipo de documento: documento electrónico Autores: Ieke Moerdijk ; SpringerLink (Online service) ; Bertrand Toën Editorial: Basel : Springer Basel Fecha de publicación: 2010 Colección: Advanced Courses in Mathematics - CRM Barcelona, ISSN 2297-0304 Número de páginas: X, 186 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0052-5 Idioma : Inglés (eng) Palabras clave: Mathematics Category theory (Mathematics) Homological algebra Algebraic topology Theory, Algebra Topology Clasificación: 51 Matemáticas Resumen: This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. Moerdijk’s lectures offer a detailed introduction to dendroidal sets, which were introduced by himself and Weiss as a foundation for the homotopy theory of operads. The theory of dendroidal sets is based on trees instead of linear orders and has many features analogous to the theory of simplicial sets, but it also reveals new phenomena. For example, dendroidal sets admit a closed symmetric monoidal structure related to the Boardman–Vogt tensor product of operads. The lecture notes start with the combinatorics of trees and culminate with a suitable model structure on the category of dendroidal sets. Important concepts are illustrated with pictures and examples. The lecture series by Toën presents derived algebraic geometry. While classical algebraic geometry studies functors from the category of commutative rings to the category of sets, derived algebraic geometry is concerned with functors from simplicial commutative rings (to allow derived tensor products) to simplicial sets (to allow derived quotients). The central objects are derived (higher) stacks, which are functors satisfying a certain up-to-homotopy descent condition. These lectures provide a concise and focused introduction to this vast subject, glossing over many of the technicalities that make the subject’s research literature so overwhelming. Both sets of lectures assume a working knowledge of model categories in the sense of Quillen. For Toën’s lectures, some background in algebraic geometry is also necessary Nota de contenido: Lectures on Dendroidal Sets -- Operads -- Trees as operads -- Dendroidal sets -- Tensor product of dendroidal sets -- A Reedy model structure on dendroidal spaces -- Boardman–Vogt resolution and homotopy coherent nerve -- Inner Kan complexes and normal dendroidal sets -- Model structures on dendroidal sets -- Simplicial Presheaves and Derived Algebraic Geometry -- Motivation and objectives -- Simplicial presheaves as stacks -- Algebraic stacks -- Simplicial commutative algebras -- Derived stacks and derived algebraic stacks -- Examples of derived algebraic stacks En línea: http://dx.doi.org/10.1007/978-3-0348-0052-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33691 Simplicial Methods for Operads and Algebraic Geometry [documento electrónico] / Ieke Moerdijk ; SpringerLink (Online service) ; Bertrand Toën . - Basel : Springer Basel, 2010 . - X, 186 p : online resource. - (Advanced Courses in Mathematics - CRM Barcelona, ISSN 2297-0304) .
ISBN : 978-3-0348-0052-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Category theory (Mathematics) Homological algebra Algebraic topology Theory, Algebra Topology Clasificación: 51 Matemáticas Resumen: This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. Moerdijk’s lectures offer a detailed introduction to dendroidal sets, which were introduced by himself and Weiss as a foundation for the homotopy theory of operads. The theory of dendroidal sets is based on trees instead of linear orders and has many features analogous to the theory of simplicial sets, but it also reveals new phenomena. For example, dendroidal sets admit a closed symmetric monoidal structure related to the Boardman–Vogt tensor product of operads. The lecture notes start with the combinatorics of trees and culminate with a suitable model structure on the category of dendroidal sets. Important concepts are illustrated with pictures and examples. The lecture series by Toën presents derived algebraic geometry. While classical algebraic geometry studies functors from the category of commutative rings to the category of sets, derived algebraic geometry is concerned with functors from simplicial commutative rings (to allow derived tensor products) to simplicial sets (to allow derived quotients). The central objects are derived (higher) stacks, which are functors satisfying a certain up-to-homotopy descent condition. These lectures provide a concise and focused introduction to this vast subject, glossing over many of the technicalities that make the subject’s research literature so overwhelming. Both sets of lectures assume a working knowledge of model categories in the sense of Quillen. For Toën’s lectures, some background in algebraic geometry is also necessary Nota de contenido: Lectures on Dendroidal Sets -- Operads -- Trees as operads -- Dendroidal sets -- Tensor product of dendroidal sets -- A Reedy model structure on dendroidal spaces -- Boardman–Vogt resolution and homotopy coherent nerve -- Inner Kan complexes and normal dendroidal sets -- Model structures on dendroidal sets -- Simplicial Presheaves and Derived Algebraic Geometry -- Motivation and objectives -- Simplicial presheaves as stacks -- Algebraic stacks -- Simplicial commutative algebras -- Derived stacks and derived algebraic stacks -- Examples of derived algebraic stacks En línea: http://dx.doi.org/10.1007/978-3-0348-0052-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33691 Ejemplares
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