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.
Higher Hida and Coleman theory for the modular curve
About the article with the same name, by G.Boxer and V.Pilloni
Boxer – Pilloni: defining families
(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.
Serre duality
About Boxer-Pilloni, section 4.3
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…