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1. Néron Models and Base Change. 1st ed. 2016
by Lars Halvard Halle, Johannes Nicaise
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2016
シリーズ名: Lecture Notes in Mathematics ; 2156
オンライン: http://dx.doi.org/10.1007/978-3-319-26638-1
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Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 Introduction
Preliminaries
Models of curves and the Neron component series of a Jacobian
Component groups and non-archimedean uniformization
The base change conductor and Edixhoven's ltration
The base change conductor and the Artin conductor
Motivic zeta functions of semi-abelian varieties
Cohomological interpretation of the motivic zeta function. /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin-top:0in; mso-para-margin-right:0in; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0in; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}
Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 Introduction
Preliminaries
Models of curves and the Neron component series of a Jacobian
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2. Quadratic Residues and Non-Residues : Selected Topics
by Steve Wright
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2016
シリーズ名: Lecture Notes in Mathematics ; 2171
オンライン: http://dx.doi.org/10.1007/978-3-319-45955-4
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Chapter 1. Introduction: Solving the General Quadratic Congruence Modulo a Prime
Chapter 2. Basic Facts
Chapter 3. Gauss' Theorema Aureum: the Law of Quadratic Reciprocity
Chapter 4. Four Interesting Applications of Quadratic Reciprocity
Chapter 5. The Zeta Function of an Algebraic Number Field and Some Applications
Chapter 6. Elementary Proofs
Chapter 7. Dirichlet L-functions and the Distribution of Quadratic Residues
Chapter 8. Dirichlet's Class-Number Formula
Chapter 9. Quadratic Residues and Non-residues in Arithmetic Progression
Chapter 10. Are quadratic residues randomly distributed?
Bibliography
Chapter 1. Introduction: Solving the General Quadratic Congruence Modulo a Prime
Chapter 2. Basic Facts
Chapter 3. Gauss' Theorema Aureum: the Law of Quadratic Reciprocity
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3. Pseudodifferential Equations Over Non-Archimedean Spaces
by W. A. Zúñiga-Galindo
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2016
シリーズ名: Lecture Notes in Mathematics ; 2174
オンライン: http://dx.doi.org/10.1007/978-3-319-46738-2
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p-Adic Analysis: Essential Ideas and Results
Parabolic-type Equations and Markov Processes
Non-Archimedean Parabolic-type Equations With Variable Coefficients
Parabolic-Type Equations on Adeles
Fundamental Solutions and Schrödinger Equations
Pseudodifferential Equations of Klein-Gordon Type
p-Adic Analysis: Essential Ideas and Results
Parabolic-type Equations and Markov Processes
Non-Archimedean Parabolic-type Equations With Variable Coefficients
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4. Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields
by Hatice Boylan
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
シリーズ名: Lecture Notes in Mathematics ; 2130
オンライン: http://dx.doi.org/10.1007/978-3-319-12916-7
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Introduction
Notations
Finite  Quadratic  Modules
Weil Representations of Finite  Quadratic  Modules
Jacobi Forms over Totally Real Number  Fields
Singular Jacobi Forms
Tables
Glossary
Introduction
Notations
Finite  Quadratic  Modules
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5. Twisted Teichmüller Curves
by Christian Weiß
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2014
シリーズ名: Lecture Notes in Mathematics ; 2104
オンライン: http://dx.doi.org/10.1007/978-3-319-04075-2
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Introduction
Background
Teichmüller Curves
Twisted Teichmüller Curves
Stabilizer and Maximality
Calculations for Twisted Teichmüller Curves
Prym Varieties and Teichmüller Curves
Lyapunov Exponents
Kobayashi Curves Revisited
Appendix
Tables
List of Symbols
Index
Bibliography
Introduction
Background
Teichmüller Curves
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6. Lectures on Formal and Rigid Geometry
by Siegfried Bosch
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2014
シリーズ名: Lecture Notes in Mathematics ; 2105
オンライン: http://dx.doi.org/10.1007/978-3-319-04417-0
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Classical Rigid Geometry
Tate Algebras
Affinoid Algebras and their Associated Spaces
Affinoid Functions
Towards the Notion of Rigid Spaces
Coherent Sheaves on Rigid Spaces
Formal Geometry
Adic Rings and their Associated Formal Schemes
Raynaud's View on Rigid Spaces
More Advanced Stuff
Appendix
References
Index
Classical Rigid Geometry
Tate Algebras
Affinoid Algebras and their Associated Spaces
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7. A Panorama of Discrepancy Theory
edited by William Chen, Anand Srivastav, Giancarlo Travaglini
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2014
シリーズ名: Lecture Notes in Mathematics ; 2107
オンライン: http://dx.doi.org/10.1007/978-3-319-04696-9
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Preface
Classical and Geometric Discrepancy
Upper Bounds in Classical Discrepancy Theory
Roth’s Orthogonal Function Method in Discrepancy Theory and Some New Connections
Irregularities of distribution and average decay of Fourier transforms
Superirregularity
Combinatorial Discrepancy
Multicolor Discrepancy of Arithmetic Structures
Algorithmic Aspects of Combinatorial Discrepancy
Practical Algorithms for Low-Discrepancy 2-Colorings
Applications and Constructions
On the distribution of solutions to diophantine equations
Discrepancy theory and quasi-Monte Carlo integration
Calculation of Discrepancy Measures and Applications
Author index
Subject index
Preface
Classical and Geometric Discrepancy
Upper Bounds in Classical Discrepancy Theory
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8. Model Theory in Algebra, Analysis and Arithmetic : Cetraro, Italy 2012, Editors: H. Dugald Macpherson, Carlo Toffalori
by Lou van den Dries, Jochen Koenigsmann, H. Dugald Macpherson, Anand Pillay, Carlo Toffalori, Alex J. Wilkie
出版情報: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014
シリーズ名: Lecture Notes in Mathematics ; 2111
オンライン: http://dx.doi.org/10.1007/978-3-642-54936-6
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Some themes around first order theories without the independence property
Lectures on the model theory of real and complex exponentiation
Lectures on the model theory of valued fields
Undecidability in number theory
Some themes around first order theories without the independence property
Lectures on the model theory of real and complex exponentiation
Lectures on the model theory of valued fields
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9. Rational Points and Arithmetic of Fundamental Groups : Evidence for the Section Conjecture
by Jakob Stix
出版情報: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013
シリーズ名: Lecture Notes in Mathematics ; 2054
オンライン: http://dx.doi.org/10.1007/978-3-642-30674-7
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Part I Foundations of Sections
1 Continuous Non-abelian H1 with Profinite Coefficients.-2 The Fundamental Groupoid
3 Basic Geometric Operations in Terms of Sections
4 The Space of Sections as a Topological Space
5 Evaluation of Units
6 Cycle Classes in Anabelian Geometry
7 Injectivity in the Section Conjecture
Part II Basic Arithmetic of Sections
8 Reduction of Sections
9 The Space of Sections in the Arithmetic Case and the Section Conjecture in Covers
Part III On the Passage from Local to Global
10 Local Obstructions at a p-adic Place
11 Brauer-Manin and Descent Obstructions
12 Fragments of Non-abelian Tate–Poitou Duality
Part IV Analogues of the Section Conjecture
13 On the Section Conjecture for Torsors
14 Nilpotent Sections
15 Sections over Finite Fields
16 On the Section Conjecture over Local Fields
17 Fields of Cohomological Dimension 1
18 Cuspidal Sections and Birational Analogues
Part I Foundations of Sections
1 Continuous Non-abelian H1 with Profinite Coefficients.-2 The Fundamental Groupoid
3 Basic Geometric Operations in Terms of Sections
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10. Intersections of Hirzebruch–Zagier Divisors and CM Cycles
by Benjamin Howard, Tonghai Yang
出版情報: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012
シリーズ名: Lecture Notes in Mathematics ; 2041
オンライン: http://dx.doi.org/10.1007/978-3-642-23979-3
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1. Introduction
2. Linear Algebra
3. Moduli Spaces of Abelian Surfaces
4. Eisenstein Series
5. The Main Results
6. Local Calculations
1. Introduction
2. Linear Algebra
3. Moduli Spaces of Abelian Surfaces