Description

Book Synopsis
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).

Table of Contents
An Overview of Serre's p-Adic Modular Forms (Miljan Brakocevic and R Sujatha); p-Adic Families of Ordinary Siegel Cusp Forms (Jacques Tilouine); Ordinary Families on Definite Unitary Groups (Baskar Balasubramanyam and Dipramit Majumdar); Modularity Lifting Theorems for Ordinary Galois Representations (David Geraghty); p-Adic L-Functions for GL(2) (Mladen Dimitrov); Arithmetic of Adjoint L-Values (Haruzo Hida); p-Adic L-Functions for GL(n) (Debargha Banerjee and A Raghuram); Non-Triviality of Generalised Heegner Cycles Over Anticyclotomic Towers: A Survey (Ashay Burungale); The Euler System of Heegner Points and p-Adic L-Functions (Ming-Lun Hsieh); Non-Commutative q-Expansions (Mahesh Kakde);

P-adic Aspects Of Modular Forms

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    A Hardback by Baskar Balasubramanyam, A Raghuram, Jacques Tilouine

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      Book details

      Publisher World Scientific Publishing Co Pte Ltd
      Published 5 August 2016
      ISBN-13 9789814719223
      978-9814719223
      ISBN-10 9814719226

      Description

      Book Synopsis
      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).

      Table of Contents
      An Overview of Serre's p-Adic Modular Forms (Miljan Brakocevic and R Sujatha); p-Adic Families of Ordinary Siegel Cusp Forms (Jacques Tilouine); Ordinary Families on Definite Unitary Groups (Baskar Balasubramanyam and Dipramit Majumdar); Modularity Lifting Theorems for Ordinary Galois Representations (David Geraghty); p-Adic L-Functions for GL(2) (Mladen Dimitrov); Arithmetic of Adjoint L-Values (Haruzo Hida); p-Adic L-Functions for GL(n) (Debargha Banerjee and A Raghuram); Non-Triviality of Generalised Heegner Cycles Over Anticyclotomic Towers: A Survey (Ashay Burungale); The Euler System of Heegner Points and p-Adic L-Functions (Ming-Lun Hsieh); Non-Commutative q-Expansions (Mahesh Kakde);

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