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SUMMARY:Kaan Bilgin (Amsterdam)
DTSTART:20240315T124000Z
DTEND:20240315T134000Z
DTSTAMP:20260423T052710Z
UID:OBAGS/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OBAGS/42/">T
 he Langlands – Kottwitz method for GSpin Shimura varieties and eigenvari
 eties</a>\nby Kaan Bilgin (Amsterdam) as part of ODTU-Bilkent Algebraic Ge
 ometry Seminars\n\n\nAbstract\nGiven a connected reductive algebraic group
  G over a number field F\, the global Langlands (reciprocity) conjecture r
 oughly predicts that\, there should be a correspondence between (automorph
 ic side) the isomorphism classes of  (cuspidal\, cohomological) automorphi
 c representations of G and (Galois side) the isomorphism classes of (irred
 ucible\, locally de-Rham) Galois representations for Gal(\\bar{F} / F) tak
 ing values in the Langlands dual group of G.\n\nIn the first part of this 
 talk\, I will sketch the main argument of our expected theorem/proof for (
 automorphic to Galois) direction of this conjecture\, for G = GSpin(n\,2)\
 , n odd and F to be totally real\, under 3 technical assumptions (for time
  being)\, namely we assume that automorphic representations are additional
 ly “non-CM” and “non-endoscopic” and “std-regular”.\n\nIn the 
 second part\, mainly following works of Loeffler and Chenevier on overconv
 ergent p-adic automorphic forms\,  I will present an idea to remove the st
 d-regular assumption on the theorem via the theory of eigenvarieties.\n
LOCATION:https://researchseminars.org/talk/OBAGS/42/
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