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SUMMARY:Brian Lawrence (Chicago)
DTSTART:20201012T230000Z
DTEND:20201012T235000Z
DTSTAMP:20260423T024758Z
UID:UCLA_NTS/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCLA_NTS/11/
 ">The Shafarevich conjecture for hypersurfaces in abelian varieties</a>\nb
 y Brian Lawrence (Chicago) as part of UCLA Number Theory Seminar\n\n\nAbst
 ract\nLet $K$ be a number field\, $S$ a finite set of primes of $O_K$\, an
 d $g$ a positive integer.  Shafarevich conjectured\, and Faltings proved\,
  that there are only finitely many curves of genus $g$\, defined over $K$ 
 and having good reduction outside $S$.  Analogous results have been proven
  for other families\, replacing "curves of genus $g$" with "K3 surfaces"\,
  "del Pezzo surfaces" etc.\; these results are also called Shafarevich con
 jectures.  There are good reasons to expect the Shafarevich conjecture to 
 hold for many families of varieties: the moduli space should have only fin
 itely many integral points.\n\nWill Sawin and I prove this for hypersurfac
 es in abelian varieties of dimension not equal to 3.\n
LOCATION:https://researchseminars.org/talk/UCLA_NTS/11/
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