BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hanlin Cai (Utah) DTSTART:20230504T210000Z DTEND:20230504T220000Z DTSTAMP:20260423T005841Z UID:UCSD_NTS/91 DESCRIPTION:Title: Perfectoid signature and local étale fundamental group\nby Hanlin C ai (Utah) as part of UCSD number theory seminar\n\nLecture held in APM 640 2 and online.\n\nAbstract\nIn this talk I'll talk about a (perfectoid) mix ed characteristic version of F-signature and Hilbert-Kunz multiplicity by utilizing the perfectoidization functor of Bhatt-Scholze and Faltings' nor malized length. These definitions coincide with the classical theory in eq ual characteristic. Moreover\, perfectoid signature detects BCM regularity and transforms similarly to F-signature or normalized volume under quasi- étale maps. As a consequence\, we can prove that BCM-regular rings have f inite local étale fundamental group and torsion part of their divisor cla ss groups. This is joint work with Seungsu Lee\, Linquan Ma\, Karl Schwede and Kevin Tucker.\n\npre-talk\n LOCATION:https://researchseminars.org/talk/UCSD_NTS/91/ END:VEVENT END:VCALENDAR