Mod-p Poincaré duality in p-adic geometry

Bogdan Zavyalov (Stanford)

23-Jul-2020, 17:00-18:20 (4 years ago)

Abstract: Étale cohomology of $\mathbf{F}_p$-local systems does not behave nicely on general smooth p-adic rigid-analytic spaces; e.g., the $\mathbf{F}_p$-cohomology of the 1-dimensional closed unit ball is infinite. However, it turns out that things are much better for proper p-adic rigid-analytic spaces. For example, Scholze used perfectoid spaces to show that proper p-adic rigid-analytic spaces have finite cohomology for any $\mathbf{F}_p$-local system. Based on Gabber's idea, I will introduce the concept of almost coherent sheaves and use it to “localize” (in an appropriate sense) some problems in the étale cohomology of rigid-analytic spaces. For example, this theory (together with perfectoid spaces) can be used to give a "new" proof of the finiteness theorem and a proof of Poincaré duality for p-torsion coefficients on smooth and proper p-adic rigid-analytic spaces.

This is work in progress.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Comments: Please note that this talk begins one hour later than the usual time.


Recent Advances in Modern p-Adic Geometry (RAMpAGe)

Series comments: The Zoom Meeting ID is: 995 3670 1681. The password for the series is: *The first three-digit prime*. Please visit the external homepage for notes and videos from past talks.

Organizers: David Hansen*, Arthur-César Le Bras*, Jared Weinstein*
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