BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Pavel Coupek (Purdue University)
DTSTART:20220201T210000Z
DTEND:20220201T220000Z
DTSTAMP:20260423T010004Z
UID:UAANTS/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/33/">
 Crystalline condition for Ainf-cohomology and ramification bounds</a>\nby 
 Pavel Coupek (Purdue University) as part of University of Arizona Algebra 
 and Number Theory Seminar\n\n\nAbstract\nLet $p>2$ be a prime and let $X$ 
 be a proper smooth formal scheme over $\\mathcal{O}_K$ where $K/\\mathbb{Q
 }_p$ is a local number field. In this talk\, we describe a series of condi
 tions $(\\mathrm{Cr}_s)$ that provide control on the Galois action on the 
 Breuil--Kisin cohomology $\\mathrm{R}\\Gamma_{\\Delta}(X/\\mathfrak{S})$ i
 nside the $A_{\\inf}$--cohomology $\\mathrm{R}\\Gamma_{\\Delta}(X_{\\mathb
 b{C}_K}/A_{\\inf})$. When $s=0$\, the resulting condition is essentially t
 he crystallinity criterion of Gee and Liu for Breuil--Kisin--Fargues $G_K$
 --modules\, and it leads to an alternative proof of crystallinity of the $
 p$--adic \\'{e}tale cohomology $H^i_{\\mathrm{et}}(X_{\\mathbb{C}_K}\, \\m
 athbb{Q}_p)$. Adapting a strategy of Caruso and Liu\, the conditions $(\\m
 athrm{Cr}_s)$ for higher $s$ then lead to upper bounds on ramification of 
 the mod $p$ \\'{e}tale cohomology $H^i_{\\mathrm{et}}(X_{\\mathbb{C}_K}\, 
 \\mathbb{Z}/p\\mathbb{Z})$\, expressed in terms of $i\, p$ and $e=e(K/\\ma
 thbb{Q}_p)$ that work without any restrictions on the size of $i$ and $e$.
 \n
LOCATION:https://researchseminars.org/talk/UAANTS/33/
END:VEVENT
END:VCALENDAR