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SUMMARY:Tom Fisher (Cambridge)
DTSTART:20240313T160000Z
DTEND:20240313T170000Z
DTSTAMP:20260418T065824Z
UID:LNTS/124
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/124/">C
 omputing the Cassels-Tate pairing on the 2-Selmer group of a genus 2 Jacob
 ian</a>\nby Tom Fisher (Cambridge) as part of London number theory seminar
 \n\nLecture held in Medawar G02 Watson.\n\nAbstract\nIn her 2021 thesis\, 
 my student Jiali Yan gave a practical method\nfor computing the Cassels-Ta
 te pairing on the 2-Selmer group of the\nJacobian of a genus 2 curve all o
 f whose Weierstrass points are rational.\nShe also gave a second method wi
 thout any assumption on the Weierstrass\npoints\, but instead assuming we 
 can find a rational point on a certain\ntwisted Kummer surface. The two me
 thods can be thought of as generalising\nmethods of Cassels and Donnelly i
 n the elliptic curve case. I will\ndescribe a practical refinement of the 
 second method which is now\nimplemented in Magma\, and has been used to un
 conditionally determine the\nranks of all genus 2 Jacobians in the LMFDB.\
 n
LOCATION:https://researchseminars.org/talk/LNTS/124/
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