Arithmetic geometry and number theory / editors, Lin Weng, Iku Nakamura.

Format:

Book

Contributor:

Weng, Lin, 1964-

Nakamura, Iku.

Series:

Series on Number Theory & Its Applications

Series on number theory and its applications ; v. 1

Language:

English

Subjects (All):

Number theory.

Algebra.

Physical Description:

1 online resource (411 p.)

Edition:

1st ed.

Place of Publication:

Hackensack, NJ : World Scientific, c2006.

Language Note:

English

Summary:

Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of specia

Contents:

Foreword; Preface; Contents; On Local y-Factors; 1 Introduction; 2 Basic Properties of Local y-Factors; 2.1 Multiplicativity; 2.2 Stability; 2.3 Remarks; 3 Local Converse Theorems; 3.1 The case of GLn(F); 3.2 A conjectural LCT; 3.3 The case of SO2n+1(F); 4 Poles of Local y-Factors; 4.1 The case of G = SO2n+1; 4.2 Other classical groups; Deligne Pairings over Moduli Spaces of Punctured Riemann Surfaces; 1 WP Metrics and TZ Metrics; 2 Line Bundles over Moduli Spaces; 3 Fundamental Relations on MgN' Algebraic Story; 4 Fundamental Relation on MgN- Arithmetic Story; 5 Deligne Tuple in General

6 Degeneration of TZ Metrics: Analytic StoryReferences; Vector Bundles on Curves over Cp; 1 Introduction; 2 Complex Vector Bundles; 3 Fundamental Groups of p-Adic Curves; 4 Finite Vector Bundles; 5 A Bigger Category of Vector Bundles; 6 Parallel Transport on Bundles in Bxcp; 7 Working Outside a Divisor on Xcp; 8 Properties of Parallel Transport; 9 Semistable Bundles; 10 A Simpler Description of Bxcp D; 11 Strongly Semistable Reduction; 12 How Big are our Categories of Bundles?; 13 Representations of the Fundamental Group; 14 Mumford Curves; References

Absolute CM-periods

Complex and p-Adic1 Introduction; 2 Notation; 2.1 Complex Theory; 2.2 p-Adic Theory; References; Special Zeta Values in Positive Characteristic; 1 Introduction; 2 Carlitz Theory; 3 Anderson-Thakur Theory; 4 t-Motives; 5 Algebraic Independence of the Special Zeta Values; References; Automorphic Forms & Eisenstein Series and Spectral Decompositions; Day One: Basics of Automorphic Forms; 1 Basic Decompositions; 1.1 Langlands Decomposition; 1.2 Reduction Theory: Siegel Sets; 1.3 Moderate Growth and Rapidly Decreasing; 1.4 Automorphic Forms; 2 Structural Results

2.1 Moderate Growth and Rapid Decreasing2.2 Semi-Simpleness; 2.3 3-Finiteness; 2.4 Philosophy of Cusp Forms; 2.5 L2-Automorphic Forms; Day Two: Eisenstein Series; 3 Definition; 3.1 Equivalence Classes of Automorphic Representations; 3.2 Eisenstein Series and Intertwining Operators; 3.3 Convergence; 4 Constant Terms of Eisenstein Series; 5 Fundamental Properties of Eisenstein Series; Day Three: Pseudo-Eisenstein Series; 6 Paley-Wiener Functions; 6.1 Paley-Wiener Functions; 6.2 Fourier Transforms; 6.3 Paley-Wiener on p; 7 Pseudo-Eisenstein Series; 8 First Decomposition of L2(G(F)\G(A))\

8.1 Inner Product Formula for P-ESes8.2 Decomposition of L2-Spaces According to Cuspidal Data; 8.3 Constant Terms of P-SEes; 9 Decomposition of Automorphic Forms According to Cuspidal Data; 9.1 Main Result; 9.2 Langlands Operators; 9.3 Key Bridge; Day Four: Spectrum Decomposition: Residual Process; 10 Why Residue?; 10.1 Pseudo-Eisenstein Series and Residual Process; 10.2 What do we have?; 10.3 Difficulties; 11 Main Results; 11.1 Functional Analysis; 11.2 Main Theorem: Rough Version; 11.3 Main Theorem: Refined Version; 11.4 How to Prove?

Day Five: Eisenstein Systems and Spectral Decomposition (II)

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786611924836

9781281924834

1281924830

9789812773531

9812773533

OCLC:

854973178