BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Livia Grammatica (Strasbourg University) DTSTART:20251105T160000Z DTEND:20251105T170000Z DTSTAMP:20260418T065553Z UID:LNTS/177 DESCRIPTION:Title: S moothness of the formal Brauer group\nby Livia Grammatica (Strasbourg University) as part of London number theory seminar\n\nLecture held in Imp erial College London\, Room 139.\n\nAbstract\nLet X be a smooth and proper variety over an algebraically closed field of characteristic p. The forma l Brauer group of X is the functor which parametrizes deformations of the trivial Brauer class of X. Under mild assumptions\, it is representable by a formal group\, closely related to the p-torsion of Br(X). We will give criteria for this formal group to be smooth in terms of the crystalline co homology of X\, thus providing a partial answer to a question of Artin-Maz ur. The strategy is to relate the formal Brauer group to crystalline cohom ology using the relationship between fppf cohomology\, crystalline cohomol ogy and the Nygaard filtration. These criteria can be used in practice to produce varieties with non-smooth formal Brauer group\, which are construc ted as higher-dimensional analogues of Igusa's surface with non-smooth Pic ard group.\n LOCATION:https://researchseminars.org/talk/LNTS/177/ END:VEVENT END:VCALENDAR