BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bjorn Poonen (Massachusetts Institute of Technology) DTSTART:20210629T142000Z DTEND:20210629T151000Z DTSTAMP:20260419T121154Z UID:AFDRT/7 DESCRIPTION:Title: Ab elian varieties of prescribed order over finite fields\nby Bjorn Poone n (Massachusetts Institute of Technology) as part of Around Frobenius dist ributions and related topics II\n\n\nAbstract\nWe give several new constru ctions of Weil polynomials to show that given a prime power q and n >> 1\, every integer in a large subinterval of the Hasse-Weil interval is realiz ed as #A(F_q) for some n-dimensional abelian variety A over F_q. Moreover \, we can make A geometrically simple\, ordinary\, and principally polariz ed. On the one hand\, our work generalizes a theorem of Howe and Kedlaya for F_2. On the other hand\, it improves upon theorems of DiPippo and How e\; Aubry\, Haloui\, and Lachaud\; and Kadets. This talk will focus on on e construction that leads to explicit (and nearly best possible) bounds\, in terms of q\, on the largest integer that is not A(F_q) for any A. This is joint work with Raymond van Bommel\, Edgar Costa\, Wanlin Li\, and Ale xander Smith.\n LOCATION:https://researchseminars.org/talk/AFDRT/7/ END:VEVENT END:VCALENDAR