Introduction to Deformations of Galois group representations (II)
El objetivo de esta charla va a ser dar una introducción a las deformaciones de representaciones de grupos de Galois: filosofia general, teoremas importantes y aplicaciones.
Varietats de Mustafin a la Hahn-Li
Bibliografia: M. A. Hahn, B. Li, arXiv 1707.01216
Higher Hida and Coleman theory for the modular curve
About the article with the same name, by G.Boxer and V.Pilloni
(Ir)rationality of Hecke L-values
Euler’s beautiful formula relating the even values of Riemann’s zeta function to Bernoulli numbers can be seen as the starting point of the investigation of special values of L-functions.
Unobstruced deformation problems for GSp(4)
Let pi be an automorphic representation of GSp(4) with an associated compatible family of p-adic Galois representations.
p-adic periods and proximity of points
Given a curve over the rational numbers of genus bigger than one, how p-adically close together can its rational points be?
Tame derivatives and the Eisenstein ideal
As was made famous by Mazur, the mod-5 Galois representation associated to the elliptic curve X_0(11) is reducible.
On the Iwasawa theory of rational elliptic curves at Eisenstein primes
Let E/Q be an elliptic curve, and p>2 a prime where E has good reduction. In the study of Iwasawa theory of E, it is common to assume that p is a non-Eisenstein prime, meaning that E[p] is irreducible as a Galois module.
Complex multiplication for real quadratic fields and p-adic modular forms of weight 3/2
I will describe how the algebraicity of the RM values of rigid meromorphic cocycles might be deduced from the study of the ordinary projections of certain p-adic modular forms of half integral weight, following an approach that is closely modelled on Gross and Zagier’s “analytic proof” of their celebrated theorem on the factorisation of differences…
Stark’s conjectures and Hilbert’s 12th Problem
In this talk we will discuss two central problems in algebraic number theory and their interconnections: explicit class field theory (also known as Hilbert’s 12th Problem), and the special values of L-functions.