BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sally Gilles DTSTART:20201104T160000Z DTEND:20201104T170000Z DTSTAMP:20260418T065400Z UID:LNTS/23 DESCRIPTION:Title: Pe riod morphisms and syntomic cohomology\nby Sally Gilles as part of Lon don number theory seminar\n\n\nAbstract\nIn 2017\, Colmez and Nizioł prov ed a comparison theorem between arithmetic p-adic nearby cycles and syntom ic cohomology sheaves. To prove it\, they gave a local construction using $(\\varphi\,\\Gamma)$-modules theory which allows to reduce the period iso morphism to a comparison theorem between Lie algebras. In this talk\, I wi ll first give the geometric version of this construction before explaining how to globalize it. This period morphism can be used to describe the é tale cohomology of rigid analytic spaces. In particular\, we deduce the se mi-stable conjecture of Fontaine-Jannsen\, which relates the étale cohom ology of the rigid analytic variety associated to a formal proper semi-sta ble scheme to its Hyodo-Kato cohomology. This result was also proved by (a mong others) Tsuji\, via the Fontaine-Messing map\, and by Česnavičius and Koshikawa\, which generalized the proof of the crystalline conjecture by Bhatt\, Morrow and Scholze. In the second part of the talk\, I will ex plain how we can use the previous map to show that the period morphism of Tsuji and the one of Česnavičius-Koshikawa are the same.\n LOCATION:https://researchseminars.org/talk/LNTS/23/ END:VEVENT END:VCALENDAR