Ramification of geometric p-adic representations in positive characteristic

Thời gian: 09:30 đến 11:00 Ngày 22/02/2022

Địa điểm: Online

Báo cáo viên: Joe Kramer-Miller, Lehigh University

Tóm tắt:

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-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.