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SUMMARY:Jef Laga
DTSTART:20210512T150000Z
DTEND:20210512T160000Z
DTSTAMP:20260418T064517Z
UID:LNTS/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/38/">Ra
 tional points and Selmer groups of genus 3 curves</a>\nby Jef Laga as part
  of London number theory seminar\n\n\nAbstract\nManjul Bhargava and Arul S
 hankar have determined the average size of the n-Selmer group of the famil
 y of all elliptic curves over Q ordered by height\, for n at most 5. They 
 used this to show that the average rank of elliptic curves is less than on
 e. \n\nIn this talk we will consider a family of nonhyperelliptic genus 3 
 curves\, and bound the average size of the 2-Selmer group of their Jacobia
 ns. This implies that a majority of curves in this family have relatively 
 few rational points. We also consider a family of abelian surfaces which a
 re not principally polarized and obtain similar results.\n
LOCATION:https://researchseminars.org/talk/LNTS/38/
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