Given a cuspidal automorphic representation of GL(n) which is
regular algebraic and conjugate self-dual, one can associate to it
a Galois representation. This Galois representation is known in
most cases to be compatible with local Langlands. When n...
To a regular algebraic cuspidal representation of GL(2) over a
quadratic imaginary field, whose central character is conjugation
invariant, Taylor et al. associated a two dimensional Galois
representation which is unramified at l different from p...
Iwasawa developed his theory for class groups in towers of
cyclotomic fields partly in analogy with Weil's theory of curves
over finite fields. In this talk, we present another such
conjectural analogy. It seems intertwined with Leopoldt's...
In this talk, I will explain my joint work with Junecue Suh on
when and why the cohomology of Shimura varieties (with nontrivial
integral coefficients) has no torsion, based on certain new
vanishing theorems we have proved. (All conditions involved...
We study families of filtered phi-modules associated to families
of p-adic Galois representations as considered by Berger and
Colmez. We show that the weakly admissible locus in a family of
filtered phi-modules is open and that the groupoid of...
The theory of (\varphi, \Gamma)-modules, which was introduced by
Fontaine in the early 90's, classifies local Galois representations
into modules over certain power series rings carrying certain extra
structures (\varphi and \Gamma). In a recent...
