Images of Galois representations and rigid tau-crystals

par Ambrus Pal

mardi 4 oct. 2016, 10:45 → 11:45 Europe/Paris

Fokko du Cloux (ICJ)

The most reasonable analogue of de Jong's conjecture on the image of representations with coefficients in local fields of characteristic p, for fundamental groups of smooth projective varieties over finite fields of characteristic p, is false in general. However the key ingredient of its proof, an analogue of the modularity conjecture in this setting, might be true. The proof of the latter uses heavily Grothendieck's six functor formalism, so in order to prove our analogue it is natural to look for a category which contains characteristic p Galois representations, but has a chance of being closed under at least some of the six operations. Based on the analogy with rigid cohomology we suggest such a category, namely rigid tau-crystals, and we establish some of its basic properties.