Ramification of geometric $p$-adic representations in positive characteristic

Joe Kramer-Miller (Lehigh University)

22-Feb-2022, 02:30-04:00 (2 years ago)

Abstract: A classical theorem of Sen describes a close relationship between the ramification filtration and the $p$-adic Lie filtration for $p$-adic representations in mixed characteristic. Unfortunately, Sen's theorem fails miserably in positive characteristic. The extensions are just too wild! There is some hope if we restrict to representations coming from geometry. Let $X$ be a smooth variety and let $D$ be a normal crossing divisor in $X$ and consider a geometric $p$-adic lisse sheaf on $X \setminus D$ (e.g. the $p$-adic Tate module of a fibration of abelian varieties). We show that the Abbes-Saito conductors along $D$ exhibit a remarkable regular growth with respect to the $p$-adic Lie filtration.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the discipline


VIASM Arithmetic Geometry Online Seminar

Organizers: Huy Dang*, Viet Cuong Do
*contact for this listing

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