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SUMMARY:Antonio Cauchi (Concordia University (Montreal))
DTSTART:20220609T101500Z
DTEND:20220609T111500Z
DTSTAMP:20260423T021426Z
UID:NTUniPD/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTUniPD/8/">
 Quaternionic diagonal cycles and instances of the Birch and Swinnerton-Dye
 r conjecture for elliptic curves over totally real fields.</a>\nby Antonio
  Cauchi (Concordia University (Montreal)) as part of Number Theory Seminar
 s at Università degli Studi di Padova\n\n\nAbstract\nIn the early ninetie
 s\, Kato’s Euler system of Beilinson elements and the theory of Heegner 
 points revolutionised the arithmetic of (modular) elliptic curves over the
  rationals. For instance\, the former led Kato to proving instances of the
  Birch and Swinnerton-Dyer conjecture for twists of elliptic curves over $
 \\Q$ by finite order characters. While the theory of Heegner points was ge
 neralised to elliptic curves $E/F$ defined over totally real number fields
 \, Kato’s result has not found its natural extension to twists of $E/F$ 
 yet. More recently\, the theory of diagonal cycles\, arising from the work
  and collective effort of Bertolini\, Darmon\, Rotger\, Seveso\, and Vener
 ucci\, has proven to be a fertile environment for proving new instances of
  the Birch and Swinnerton-Dyer conjecture for elliptic curves over the rat
 ionals. The aim of this talk is to discuss joint work in progress with Dan
 iel Barrera\, Santiago Molina\, and Victor Rotger on the generalisation of
  the theory of diagonal cycles to quaternionic Shimura curves over totally
  real number fields $F$ and its application to extending Kato’s result f
 or twists of elliptic curves $E/F$ by Hecke characters of $F$ of finite or
 der.\n
LOCATION:https://researchseminars.org/talk/NTUniPD/8/
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