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SUMMARY:Kiran Kedlaya (UCSD)
DTSTART:20211007T210000Z
DTEND:20211007T220000Z
DTSTAMP:20260423T022808Z
UID:UCSD_NTS/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/42/
 ">Orders of abelian varieties over F_2</a>\nby Kiran Kedlaya (UCSD) as par
 t of UCSD number theory seminar\n\nLecture held in APM 7321 and online.\n\
 nAbstract\nWe describe several recent results on orders of abelian varieti
 es over $\\mathbb{F}_2$: every positive integer occurs as the order of an 
 ordinary abelian variety over $\\mathbb{F}_2$ (joint with E. Howe)\; every
  positive integer occurs infinitely often as the order of a simple abelian
  variety over $\\mathbb{F}_2$\; the geometric decomposition of the simple 
 abelian varieties over $\\mathbb{F}_2$ can be described explicitly (joint 
 with T. D'Nelly-Warady)\; and the relative class number one problem for fu
 nction fields is reduced to a finite computation (work in progress).\n\nAl
 l of these results rely on the relationship between isogeny classes of abe
 lian varieties over finite fields and Weil polynomials given by the work o
 f Weil and Honda-Tate. With these results in hand\, most of the work is to
  construct algebraic integers satisfying suitable archimedean constraints.
 \n\nTalk to be given in person and streamed via Zoom.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/42/
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