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Presented By: Group, Lie and Number Theory Seminar - Department of Mathematics

GLNT: Ramification bounds via Wach modules and q-crystalline cohomology

Pavel Coupek (Michigan State)

Given a Galois representation T obtained as the mod p etale cohomology of a smooth proper variety with good reduction over a p-adic field K, Breuil-Kisin cohomology can be used to obtain a bound on ramification of T. Under the assumption that K is absolutely unramified, I will describe an alternative approach to obtaining such a bound using Wach modules and q–crystalline cohomology. The resulting bound is stronger than the one obtained via Breuil-Kisin theory, and in particular, it is able to distinguish the good reduction case from the more general case of semistable reduction.

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