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SUMMARY:Mordell–Weil groups of elliptic curves — beyond ranks - Alex B
 artel\, University of Glasgow
DTSTART:20220308T143000Z
DTEND:20220308T153000Z
UID:TALK169484@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:If _E_/*Q* is an elliptic curve\, and _F_/*Q* is a finite Galo
 is extension\, then _E_(_F_)\nis not merely a finitely generated abelian g
 roup\, but also a Galois module. If we fix\na finite group _G_\, and let _
 F_ vary over all _G_-extensions\, then what can we say about the\nstatisti
 cal behaviour of _E_(_F_) as a *Z*[_G_]-module? In this talk I will report
  on joint\nwork with Adam Morgan\, in which we investigate a special case 
 of this very general\nquestion. Our work has surprising connections to que
 stions about frequency of failure\nof the Hasse principle for genus 1 hype
 relliptic curves\, as well as to Stevenhagen's\nconjecture on the solubili
 ty of the negative Pell equation.
LOCATION:MR13
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