Journée arithmétique à Villetaneuse
Organisateurs: P. Boyer, F.
Brumley, J. Tilouine
Les participants seront invités à déjeuner au restaurant administratif.
L'inscription n'est pas obligatoire mais si vous pouvez cliquer sur
le lien suivant pour nous avertir de votre participation.
Programme:
9h-10h Sundeep Balaji (post doc Heidelberg)
Title: G-valued potentially semi-stable deformation rings
Résumé: For a reductive group G and a local field K, consider the
universal deformation ring of a G-valued representation of the absolute
Galois group of K. We show that the subset of potentially semi-stable or
potentially crystalline deformations with a given fixed Hodge type and
Galois type cuts out a closed subscheme of its generic fiber. We show
that the potentially crystalline deformation ring is formally smooth and
compute its dimension. We apply this to study a global deformation ring
and give a presentation with an interesting property.
10h15-11h15 Jean-Marc Fontaine (Université Paris 11)
Title: Faisceaux de p-torsion et Q_p faisceaux en caractéristique p
Résumé: Je
tenterai d'esquisser la construction de faisceaux de p-torsion en
caractéristique p qui généralisent les schémas en groupe finis (travail
en commun avec Uwe Jannsen) et d'expliquer comment les Q_p-faisceaux
qu'on en déduit sont liés aux Q_p-schémas que j'ai construit avec
Laurent Fargues.
11h15-11h45 Pause café et croissants
11h45-12h45 David Hansen (post doc à IMJ)
Title: A modularity conjecture for trianguline Galois representations
Résumé: I'll
formulate a precise modularity conjecture relating n-dimensional
trianguline representations of Gal(Qbar/Q) with Hecke eigenclasses in
overconvergent cohomology on GL_n/Q, in the spirit of the
Clozel/Fontaine-Mazur/Langlands conjecture. When n=2, this conjecture
follows from results of Bellaiche, Emerton and Stevens; I'll explain
this deduction, as well as the proofs of some special cases when
n>2. Time permitting, I'll try to frame these results in the
broader context of eigenvarieties and the p-adic Langlands program.
12h45-14h déjeuner au self
14h-15h Wushi Goldring (Post doc à l'université Paris 13)
Title: Invariants de Hasse sur les strates de
Ekedahl-Oort avec applications à la correspondance de Langlands dans
le cas irrégulier (Travail en commun avec D. Geraghty)
15h15-16h15 Ben Moonen (Radboud University Nijmegen)
Title: Modified diagonalsRésumé:
I'll talk about joint work in progress with Qizheng YIN concerning
modified diagonal classes. Given a variety X with a base point, these
are classes Gamma^m on X^m that are modifications of the small
diagonal. They were first studied by Gross and Schoen, who proved some
vanishing results on curves. Meanwhile we have some further examples of
vanishing results for modified diagonals, including a very beautiful
result of Beauville and Voisin for K3 surfaces. O'Grady proved some
further results about modified diagonals. We reprove some of his
results with different techniques, taking a motivic perspective. We
show that Voevodsky's smash-nilpotence conjecture implies that for any
variety X, if we take m big enough, Gamma^m should vanish in the Chow
ring. We also prove a number of results that are part of an attempt to
prove this conclusion unconditionally.
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