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SUMMARY:Bas Edixhoven (Universiteit Leiden)
DTSTART:20200504T180000Z
DTEND:20200504T185000Z
DTSTAMP:20260423T024803Z
UID:UCLA_NTS/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCLA_NTS/7/"
 >Geometric quadratic Chabauty</a>\nby Bas Edixhoven (Universiteit Leiden) 
 as part of UCLA Number Theory Seminar\n\n\nAbstract\nJoint work with Guido
  Lido (see arxiv preprint). Determining all rational points on a curve of 
 genus at least 2 can be difficult. Chabauty's method (1941) is to intersec
 t\, for a prime number p\, in the p-adic Lie group of p-adic points of the
  jacobian\, the closure of the Mordell-Weil group with the p-adic points o
 f the curve. If the Mordell-Weil rank is less than the genus then this met
 hod has never failed. Minhyong Kim's non-abelian Chabauty programme aims t
 o remove the condition on the rank. The simplest case\, called quadratic C
 habauty\, was developed by Balakrishnan\, Dogra\, Mueller\, Tuitman and Vo
 nk\, and applied in a tour de force to the so-called cursed curve (rank an
 d genus both 3). Our work aims to make the quadratic Chabauty method small
  and geometric again\, by describing it in terms of only "simple algebraic
  geometry" (line bundles over the jacobian and models over the integers).\
 n
LOCATION:https://researchseminars.org/talk/UCLA_NTS/7/
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