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SUMMARY:John Voight (Dartmouth)
DTSTART:20210317T160000Z
DTEND:20210317T170000Z
DTSTAMP:20260423T021351Z
UID:hnts/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/hnts/25/">Co
 unting elliptic curves with torsion\, and a probabilistic local-global pri
 nciple</a>\nby John Voight (Dartmouth) as part of Heilbronn number theory 
 seminar\n\n\nAbstract\nCan we detect torsion of a rational elliptic curve 
 $E$ by looking modulo primes?  Well\, for almost all primes $p$\, the tors
 ion subgroup $E(\\mathbb{Q})_{\\operatorname{tor}}$ maps injectively into 
 $E(\\mathbb{F}_p)$\; but the converse statement holds only up to isogeny\,
  by a theorem of Katz.  In this\ntalk\, we consider a probabilistic refine
 ment for the elliptic curves themselves: if $m | \n \\#E(\\mathbb{F}_p)$ f
 or almost all primes $p$\, what is the probability that $m | \\#E(\\mathbb
 {Q})_{\\operatorname{tor}}$?  We answer this question in a precise way by 
 giving an asymptotic count of rational elliptic curves by height with cert
 ain prescribed Galois image.\n\nThis is joint work with John Cullinan and 
 Meagan Kenney.\n
LOCATION:https://researchseminars.org/talk/hnts/25/
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