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SUMMARY:Christopher Skinner (Princeton University)
DTSTART:20260210T203000Z
DTEND:20260210T213000Z
DTSTAMP:20260419T151454Z
UID:BC-MIT/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BC-MIT/29/">
 Euler systems and relative cohomology</a>\nby Christopher Skinner (Princet
 on University) as part of BC-MIT number theory seminar\n\nLecture held in 
 2-449 at MIT.\n\nAbstract\nEuler systems -- organized collections of Galoi
 s cohomology classes for arithmetically interesting p-adic Galois represen
 tations -- have been a useful tool for establishing the conjectured relati
 on between special values of L-functions and the ranks and orders of Selme
 r groups when they exist.  In this talk I will describe recent work provid
 ing new examples of Euler systems with cyclotomic variation\, including an
  Euler system for the symmetric square of a modular form.  As a replacemen
 t for the motivic origin of prior examples\, we find the Galois extensions
  in the relative cohomology of Shimura varieties. The control needed to es
 tablish the norm relations and make connections with L-values is provided 
 by recent results in integral p-adic Hodge theory\, allowing explicit conn
 ection with holomorphic automorphic forms.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/29/
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