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SUMMARY:Jef Laga (University of Cambridge)
DTSTART:20210215T130000Z
DTEND:20210215T133000Z
DTSTAMP:20260423T052832Z
UID:POINT/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POINT/27/">S
 elmer groups of some families of genus 3 curves and abelian surfaces</a>\n
 by Jef Laga (University of Cambridge) as part of POINT: New Developments i
 n Number Theory\n\n\nAbstract\nManjul Bhargava and Arul Shankar have deter
 mined the average size of the $n$-Selmer group of the family of all ellipt
 ic curves over $\\mathbb{Q}$ ordered by height\, for $n$ at most $5$. In t
 his talk we will consider a family of nonhyperelliptic genus $3$ curves\, 
 and bound the average size of the $2$-Selmer group of their Jacobians. Thi
 s implies that a majority of curves in this family have relatively few rat
 ional points. We also consider a family of abelian surfaces which are not 
 principally polarized and obtain similar results. The proof is a combinati
 on of the theory of simple singularities\, graded Lie algebras and orbit-c
 ounting techniques.\n
LOCATION:https://researchseminars.org/talk/POINT/27/
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