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SUMMARY:Nils Bruin (Simon Fraser) and Daniel Lewis (University of Arizona)
DTSTART:20200630T173000Z
DTEND:20200630T180000Z
DTSTAMP:20260423T195930Z
UID:ANTS14/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ANTS14/7/">T
 wo-cover descent on plane quartics with rational bitangents</a>\nby Nils B
 ruin (Simon Fraser) and Daniel Lewis (University of Arizona) as part of Al
 gorithmic Number Theory Symposium (ANTS XIV)\n\n\nAbstract\nWe implement t
 wo-cover descent for plane quartics over $\\Q$ with all 28 bitangents rati
 onal and show that on a significant collection of test cases\, it resolves
  the existence of rational points. We also review a classical description 
 of the relevant moduli space and use it to generate examples. We observe t
 hat local obstructions are quite rare for such curves\, and only seem to o
 ccur in practice at primes of good reduction. In particular\, having good 
 reduction at 11 implies having no rational points. We also gather numerica
 l data on two-Selmer ranks of Jacobians of these curves\, which suggests t
 hat these often have non-trivial Tate-Shafarevich groups.\n\nChairs: Tom F
 isher and Jen Paulhus\n
LOCATION:https://researchseminars.org/talk/ANTS14/7/
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