BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Wanlin Li (Washington University in St. Louis) DTSTART:20231012T200000Z DTEND:20231012T210000Z DTSTAMP:20260423T052457Z UID:NTC/28 DESCRIPTION:Title: Bas ic reductions of abelian varieties\nby Wanlin Li (Washington Universit y in St. Louis) as part of Lethbridge number theory and combinatorics semi nar\n\nLecture held in University of Lethbridge: M1060 (Markin Hall).\n\nA bstract\nGiven an abelian variety $A$ defined over a number field\, a conj ecture attributed to Serre states\nthat the set of primes at which $A$ adm its ordinary reduction is of positive density. This conjecture had been pr oved for elliptic curves (Serre\, 1977)\, abelian surfaces (Katz 1982\, Sa win 2016) and certain higher dimensional abelian varieties (Pink 1983\, Fi te 2021\, etc).\n\nIn this talk\, we will discuss ideas behind these resul ts and recent progress for abelian varieties with non-trivial endomorphism s\, including the case where $A$ has almost complex multiplication by an a belian CM field\, based on joint work with Cantoral-Farfan\, Mantovan\, Pr ies\, and Tang.\n\nApart from ordinary reduction\, we will also discuss th e set of primes at which an abelian variety admits basic reduction\, gener alizing a result of Elkies on the infinitude of supersingular primes for e lliptic curves. This is joint work with Mantovan\, Pries\, and Tang.\n LOCATION:https://researchseminars.org/talk/NTC/28/ END:VEVENT END:VCALENDAR