P-adic Aspects Of Modular Forms

by Baskar Balasubramanyam, A Raghuram, Jacques Tilouine, Haruzo Hida

Overview

The aim of this book is to give a systematic exposition of results in some important cases where p-adic families and p-adic L-functions are studied. We first look at p-adic families in the following cases: general linear groups, symplectic groups and definite unitary groups. We also look at applications of this theory to modularity lifting problems. We finally consider p-adic L-functions for GL(2), the p-adic adjoint L-functions and some cases of higher GL(n).

Product Details

ISBN-13:	9789814719223
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	08/05/2016
Edition description:	New Edition
Pages:	344
Product dimensions:	6.10(w) x 9.10(h) x 0.90(d)

Table of Contents

Preface v

1 An overview of Serre's p-adic modular forms Miljan Brakocevic R. Sujatha 1

2 p-adic families of ordinary Siegel cusp forms J. Tilouine 23

3 Ordinary families of automorphic forms on definite unitary groups Baskar Balasubramanyam Dipramlt Majumdar 65

4 Notes on modularity lifting in the ordinary case David Geraghty 121

5 p-adic L-functions for Hilbert modular forms Mladem Dimilrov 165

6 Arithmetic of adjoint L-values Haruzo Hida 185

7 p-adir L-functions for Gl Debargha Banerjee A. Raghuram 237

8 Non-triviality of generalised Heegner cycles over anticyclotomic towers: a survey Ashay A. Burungale 279

9 The Euler system of Heegner points and p-adic L-functions Ming-Lun Hsieh 307

10 Non-commutative q-expansions Mahesh Kakde 317