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SUMMARY:Adam Morgan (University of Glasgow)
DTSTART:20211203T150000Z
DTEND:20211203T160000Z
DTSTAMP:20260423T024756Z
UID:QMULANTS/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QMULANTS/21/
 ">Integral Galois module structure of Mordell--Weil groups</a>\nby Adam Mo
 rgan (University of Glasgow) as part of Queen Mary University of London Al
 gebra and Number Theory Seminar\n\n\nAbstract\nLet E/Q be an elliptic curv
 e\, G a finite group and V a fixed finite dimensional rational representat
 ion of G. As we run over G-extensions F/Q with E(F)⊗Q isomorphic to V \,
  how does the Z[G]-module structure of E(F) vary from a statistical point 
 of view? I will report on joint work with Alex Bartel in which we propose 
 a heuristic giving a conjectural answer to an instance of this question\, 
 and make progress towards its proof. In the process I will relate the ques
 tion to quantifying the failure of the Hasse principle in certain families
  of genus 1 curves\, and explain a close analogy between these heuristics 
 and Stevenhagen's conjecture on the solubility of the negative Pell equati
 on.\n
LOCATION:https://researchseminars.org/talk/QMULANTS/21/
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