Number Theory Seminar - Spring 2023

Eigenvarieties and p-adic L-functions

I organised a seminar at Columbia University on eigenvarieties and their role in the study of p-adic L-functions. The main reference is Bellaïche's book [Bel21]. The initial plan is to cover at least the first two parts of this textbook and some of the third part. Another reference is Bellaïche and Chevenier's work [BC09] on families of Galois representations.
Relevant information
Time: Wednesday, 11:40am-12:55pm
Room : MATH 528
Date Title Speaker Reference Notes
February 08 Introduction to Eigenalgebras and Eigenvarieties (Abstract) David Marcil [Bel21, (2.7)-(3.3)]
February 15 Properties and Machinery of Eigenvarieties (Abstract) David Marcil [Bel21, (3.3)-(3.9)]
February 22 Modular Symbols and Cohomology (Abstract) David Marcil [Bel21, Ch. 4]
March 01 Classical Modular Symbols and Modular Forms (Abstract) David Marcil
March 08 The Fréchet module of Overconvergent Distributions (Abstract) Jiahe Shen [Bel21, (6.1)-(6.3)]
March 15 Spring break - No talk
March 22 Hecke action on Distributions and Overconvergent Modular Symbols (Abstract) Jiahe Shen [Bel21, (6.3)-(6.5)]
March 29 Applications to p-adic L-functions of Non-Critical Slope Modular Forms (Abstract) David Marcil [Bel21, (6.5)-(6.7)] PDF
April 05 The Eigencurve of Overconvergent Modular Symbols and the Coleman-Mazur Eigencurve (Abstract) David Marcil [Bel21, (7.1)-(7.2)] PDF
April 12 Classical Points and Galois Representations (Abstract) David Marcil [Bel21, (7.3)-(7.6)] PDF
April 19 Local Geometry of the Eigencurve of Modular Symbols (Abstract) David Marcil [Bel21, (7.6)-(7.7)] PDF
April 26 p-adic L-functions on the Eigencurve (Abstract) David Marcil [Bel21, Ch. 8] PDF
May 03 Adjoint p-adic L-function on the Cuspidal Eigencurve (Abstract) David Marcil [Bel21, Ch. 9] PDF
[Bel21] - BELLAÏCHE, Joël - The Eigenbook : Eigenvarieties, families of Galois representations, p-adic L-functions
[BC09] - BELLAÏCHE, J. CHEVENIER, G. - Families of Galois representations and Selmer groups