Arithmetic of L-Functions ; Proceedings of an International Conference held at ICMAT, Madrid, May 2023.

Format:

Book

Author/Creator:

Bullach, Editor.

Contributor:

Macías Castillo, Editor.

Series:

EMS series of congress reports.

EMS Series of Congress Reports (ecr) 20 2523-5168

Language:

English

Subjects (All):

Arithmetic--History.

Arithmetic.

Physical Description:

1 online resource (366 pages)

Place of Publication:

EMS Press 2025

Berlin : EMS Press, 2025.

System Details:

text file PDF

Summary:

This volume brings together research and survey articles in algebraic number theory and arithmetic geometry. All of them share as a general theme the mysterious connections between special values of -functions and algebraic invariants of Galois representations. These relationships are explored primarily through the lenses of Iwasawa theory and other Galois-equivariant points of view. The topics covered include the Galois module structure of ideal class groups, reciprocity laws in Iwasawa theory, Euler systems, -adic -functions, and étale cohomology - each of which has had a remarkable importance in the study of -adic Galois representations over the last few decades. In addition, the final chapters of this volume serve as an introduction to the emerging subject of special -values in positive characteristic. This is a new direction in the general area of global function field arithmetic that is concerned with the invariants of Galois representations valued in positive characteristic, as provided by Drinfeld modules or -modules. Serving as the proceedings of an international conference held at ICMAT (Madrid) in May 2023, this volume is a useful resource for important techniques and approaches, as well as a source of concrete results and bibliographic references. It is of interest both to established researchers and to graduate students interested in algebraic number theory or in arithmetic geometry.

Contents:

Front matter

Preface

Contents

On functional equations of Euler systems

On the Artin formalism for triple product p-adic L‑functions: Chow-Heegner points vs. Heegner points

Character formula for conjugacy classes in a coset

Character formula for Weil representations in terms of Frobenius traces

On the Galois module structure of minus class groups

On class groups and Iwasawa modules of CM-fields

On natural complexes in Iwasawa theory

Explicit reciprocity laws in Iwasawa theory: A survey with some focus on the Lubin-Tate setting

On the formal Carlitz module

An equivariant Tamagawa number formula for abelian t-modules and applications

Euler factors of equivariant L-functions of Drinfeld modules and beyond

List of contributors.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783985475841

3985475849