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UID:news1268@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20211125T141706
DTSTART;TZID=Europe/Zurich:20211202T170000
SUMMARY:Number Theory Web Seminar: Kiran Kedlaya (University of California 
 San Diego)
DESCRIPTION:We 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). All o
 f these results rely on the relationship between isogeny classes of abelia
 n varieties over finite fields and Weil polynomials given by the work of W
 eil and Honda-Tate. With these results in hand\, most of the work is to co
 nstruct algebraic integers satisfying suitable archimedean constraints.\\r
 \\nFor further information about the seminar\, please visit this webpage [
 https://www.ntwebseminar.org/].
X-ALT-DESC:<p>We describe several recent results on orders of abelian varie
 ties over $\\mathbb{F}_2$: every positive integer occurs as the order of a
 n ordinary abelian variety over $\\mathbb{F}_2$ (joint with E. Howe)\; eve
 ry positive integer occurs infinitely often as the order of a simple abeli
 an variety over $\\mathbb{F}_2$\; the geometric decomposition of the simpl
 e abelian varieties over $\\mathbb{F}_2$ can be described explicitly (join
 t with T. D'Nelly-Warady)\; and the relative class number one problem for 
 function fields is reduced to a finite computation (work in progress). All
  of these results rely on the relationship between isogeny classes of abel
 ian varieties over finite fields and Weil polynomials given by the work of
  Weil and Honda-Tate. With these results in hand\, most of the work is to 
 construct algebraic integers satisfying suitable archimedean constraints.<
 /p>\n<p>For further information about the seminar\, please visit this<a hr
 ef="https://www.ntwebseminar.org/"> webpage</a>.</p>
DTEND;TZID=Europe/Zurich:20211202T180000
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