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SUMMARY:Samuel Mundy (Princeton University)
DTSTART:20250211T210000Z
DTEND:20250211T220000Z
DTSTAMP:20260423T130421Z
UID:MITNT/109
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/109/">
 Vanishing of Selmer groups for Siegel modular forms</a>\nby Samuel Mundy (
 Princeton University) as part of MIT number theory seminar\n\nLecture held
  in Room 2-449 in the Simons Building (building 2).\n\nAbstract\nLet $\\pi
 $ be a cuspidal automorphic representation of $Sp_{2n}$ over $\\mathbb{Q}$
  which is holomorphic discrete series at infinity\, and $\\chi$ a Dirichle
 t character. Then one can attach to $\\pi$ an orthogonal $p$-adic Galois r
 epresentation $\\rho$ of dimension $2n+1$. Assume $\\rho$ is irreducible\,
  that $\\pi$ is ordinary at $p$\, and that $p$ does not divide the conduct
 or of $\\chi$. I will describe work in progress which aims to prove that t
 he Bloch--Kato Selmer group attached to $\\rho\\otimes\\chi$ vanishes\, un
 der some mild ramification assumptions on $\\pi$\; this is what is predict
 ed by the Bloch--Kato conjectures.\n\nThe proof uses "ramified Eisenstein 
 congruences" by constructing $p$-adic families of Siegel cusp forms degene
 rating to Klingen Eisenstein series of nonclassical weight\, and using the
 se families to construct ramified Galois cohomology classes for the Tate d
 ual of $\\rho\\otimes\\chi$.\n
LOCATION:https://researchseminars.org/talk/MITNT/109/
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