BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Steven Groen (UvA University of Amsterdam) DTSTART:20251203T160000Z DTEND:20251203T170000Z DTSTAMP:20260418T065334Z UID:LNTS/175 DESCRIPTION:Title: E kedahl-Oort strata of double covers in characteristic 2.\nby Steven Gr oen (UvA University of Amsterdam) as part of London number theory seminar\ n\nLecture held in Imperial College London\, Room 139.\n\nAbstract\nThis t alk concerns a variant of the Schottky problem\, which asks to classify Ja cobians among all abelian varieties. In characteristic p\, there is a rich extra structure to consider. Namely\, in characteristic p\, abelian varie ties can be partitioned into so-called Ekedahl-Oort strata\, within which all abelian varieties have isomorphic p-torsion group schemes. From this p oint of view\, it is fruitful to investigate which p-torsion group schemes can occur as the p-torsion of the Jacobian of a (specified type of) curve . In this talk\, we treat the 2-torsion of curves in characteristic 2 that admit a separable double cover to another curve. Through an analysis of t he first De Rham cohomology\, we prove that the p-torsion of a double cove r of an ordinary curve is determined by the ramification breaks of the cov er. This generalizes a result by Elkin and Pries\, where the base curve is the projective line and the covers are hyperelliptic curves. When the bas e curve is not ordinary\, we establish bounds on the Ekedahl-Oort type of the cover.\n LOCATION:https://researchseminars.org/talk/LNTS/175/ END:VEVENT END:VCALENDAR