BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bogdan Zavyalov (Stanford) DTSTART:20200723T170000Z DTEND:20200723T182000Z DTSTAMP:20260423T035751Z UID:RAMpAGe/6 DESCRIPTION:Title: Mod-p Poincaré duality in p-adic geometry\nby Bogdan Zavyalov (Stanfo rd) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAb stract\nÉtale cohomology of $\\mathbf{F}_p$-local systems does not behav e nicely on general smooth p-adic rigid-analytic spaces\; e.g.\, the $\\ma thbf{F}_p$-cohomology of the 1-dimensional closed unit ball is infinite. H owever\, 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 $\\mat hbf{F}_p$-local system. Based on Gabber's idea\, I will introduce the conc ept of almost coherent sheaves and use it to “localize” (in an appropr iate sense) some problems in the étale cohomology of rigid-analytic space s. 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-analy tic spaces.\n\nThis is work in progress.\n\nPlease note that this talk beg ins one hour later than the usual time.\n LOCATION:https://researchseminars.org/talk/RAMpAGe/6/ END:VEVENT END:VCALENDAR