BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Shichen Tang (UC Irvine) DTSTART:20220412T210000Z DTEND:20220412T220000Z DTSTAMP:20260423T024755Z UID:UAANTS/38 DESCRIPTION:Title: Slope stability for higher rank Artin--Schreier--Witt towers\nby Shich en Tang (UC Irvine) as part of University of Arizona Algebra and Number Th eory Seminar\n\n\nAbstract\nFor a curve in characteristic p\, consider the p-adic valuations of the reciprocal roots of its zeta function. These are rational numbers between 0 and 1\, and they are also the slopes of the p- adic Newton polygon of the numerator polynomial of the zeta function. In g eneral\, these numbers depend on the curve\, and all we have is an upper b ound and a lower bound for the Newton polygon. But for curves in an Artin- -Schreier--Witt tower satisfying certain conditions\, the slopes behave in a stable way. It can be shown that the data of the slopes of the Newton p olygon for all the curves in the tower is determined by the data for finit ely many curves\, and for each curve\, the slopes can be explicitly writte n as a union of finitely many arithmetic progressions.\n\nLet d be the ran k of the Galois group of this tower as a free Z_p-module. In rank d=1 case \, this was proved by Kosters--Zhu in 2017. In this talk\, we will explain the proof for the higher rank case.\n LOCATION:https://researchseminars.org/talk/UAANTS/38/ END:VEVENT END:VCALENDAR