Schedule

Program

T. Berger (Cambridge, GB) : Modularity of residually reducible Galois representations of imaginary quadratic fields
Abstract: We present an R=T theorem for deformations of residually reducible Galois representations of imaginary quadratic fields. This is a joint work with K. Klosin.

O. Brinon (Univ. Paris 13): Overconvergence of p-adic monodromy

F. Calegari (Northwestern U.): Borel-Wallach Vanishing and potential modularity

G. Chenevier (CNRS, École Polytechnique): The infinite fern of Galois representations of type U(3)
Abstract: Let E be a CM field, r a mod. p Galois representation of the absolute Galois group of E, which is self-dual conjugate ("of type U(3)") and X(r) the universal deformation space of r of type U(3). If r is "modular" and "unobstructed", we show that the modular points are Zariski-dense in X(r).

C.-L. Chai (UPenn) CM liftings of abelian varieties
Abstract: Given an abelian variety B over a finite field k, consider the three statements
(CML) B admits a CM lifting in characteristic zero;
(NI) There exists an abelian variety A isogenous to B over k which admits a CM lifting to a discrete valuation ring;
(I) There exists A isogenous to B over k which admits a CM lifting in characteristic zero.
In a joint work with B. Conrad and F. Oort, we show that (CML) may fail in general, (NI) is equivalent to the "residual reflex condition" for B, and (I) is true.

P. Colmez (École Polytechnique): Sur la correspondance de Langlands p-adique pour GL₂(Q_p)

L. Fargues (CNRS, Univ. Paris 11): Harder-Narasimhan filtration for finite flat group schemes and higher canonical subgroups

E. Ghate (TIFR, Mumbai): Adjoint lifts and modular endomorphisms algebras
Abstract: In a joint work with C. Banerjee, we show how the slopes of the Gelbart-Jacquet lift of a modular form do control the ramification of the endomorphism algebra of the motive M_f attached to f.

F. Herzig (Northwestern U.): Serre weights for U(3)

H. Hida (UCLA): Vanishing of the mu-invariant of Katz p-adic L-function

M.-L. Hsieh (McMaster and Nat. Taiwan U.): p-adic modular forms on U(3) and Iwasawa Main Conjecture for CM fields

A. Iovita (Concordia U. and Padova U.): Comparison isomorphisms for formal schemes
Abstract: Let K be a finite unramified extension of Q_p and X be a proper smooth scheme over O_K. In a joint work with F. Andreatta, we developed a method for proving comparison isomorphisms comparing etale cohomology of the generic fiber of X with the crystalline cohomology of the special fiber after extending scalars to B_cris. The method extends to the case of non-proper smooth formal schemes. As application, we have a cohomological construction of p-adic families of modular forms.

T. Itô (Univ. de Kyôto): TBA

P. Kassaei (Kings College, UK): Canonical subgroups on Hilbert modular varieties (joint with E. Goren)

M.-H. Nicole (Paris 7): Traverso's truncation conjectures and refinements of the Newton polygon stratification.
Abstract: Circa 1979, C. Traverso conjectured sharp quantitative bounds to determine a p-divisible group up to isogeny (resp. up to isomorphism). This talk will report on the thornier isomorphism conjecture, which is wrong in general, in contrast with the isogeny conjecture (proved by Vasiu and the speaker in 2006). We will also describe the behaviour of the isogeny cutoff and isomorphism number in families, giving rise to natural stratifications of Newton polygon strata. Joint work with E. Lau, A. Vasiu.

V. Pilloni (Univ. Paris 13): TBA

S. Sasaki (Cambridge U.): On Artin representations and nearly ordinary Hecke algebras over totally real fields

Abstract: I will explain how to prove an analogue in the ``completely split'' Hilbert case of a result of Buzzard and Taylor about Artin representations and weight one forms.

M. Schein (Bar-Ilan U.): On the Buzzard-Diamond-Jarvis conjecture

Y.-C. Tian (IAS and Princeton U.): Higher canonical subgroups

M.-F. Vignéras (U. Paris 7): Towards a p-adic Langlands correspondence for p-adic reductive groups