Wojciech J. Gajda

Abstract:

If X is a variety over an equicharacteristic local field F, and l is a prime different from the residue characteristic p, then one can use the l-adic local monodromy theorem and the theory of Weil-Deligne representations to make precise the conjecture that the l-adic etale cohomology groups are independent of l. I will explain how to extend this conjecture to include the case l=p, and then show how to prove (a weak form of it) it when X is smooth and proper over F, via a 'spreading out' argument. I will also discuss similar questions for the unipotent fundamental group. This is joint work with Bruno Chiarellotto.