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SUMMARY:Óscar Rivero (University of Warwick)
DTSTART:20210519T150000Z
DTEND:20210519T160000Z
DTSTAMP:20260423T022734Z
UID:RSVP/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RSVP/5/">Eis
 enstein congruences and Euler systems</a>\nby Óscar Rivero (University of
  Warwick) as part of Rendez-vous on special values and periods\n\n\nAbstra
 ct\nLet $f$ be a cuspidal eigenform of weight two\, and let $p$ be a prime
  at which $f$ is congruent to an Eisenstein series. Beilinson constructed 
 a class arising from the cup-product of two Siegel units and proved a rela
 tionship with the first derivative of the $L$-series of $f$ at the near ce
 ntral point $s=0$. I will motivate the study of congruences between modula
 r forms at the level of cohomology classes\, and will report on a joint wo
 rk with Victor Rotger where we prove two congruence formulas relating the 
 Beilinson class with the arithmetic of circular units. The proofs make use
  of delicate Galois properties satisfied by various integral lattices and 
 exploits Perrin-Riou's\, Coleman's and Kato's work on the Euler systems of
  circular units and Beilinson-Kato elements and\, most crucially\, the wor
 k of Fukaya-Kato.\n
LOCATION:https://researchseminars.org/talk/RSVP/5/
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