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SUMMARY:Variation under functoriality of geometrically-motivated classes o
 f archimedean representations - Wushi Goldring (Stockholm University)
DTSTART:20171128T143000Z
DTEND:20171128T153000Z
UID:TALK78651@talks.cam.ac.uk
CONTACT:Beth Romano
DESCRIPTION:Among the circle of conjectures which forms the global\nLangla
 nds correspondence\, perhaps the simplest is the prediction that\nthe Heck
 e eigenvalues of L and C-algebraic automorphic representations \\pi\nare a
 lgebraic numbers. Fundamental to our current understanding of\nthis conjec
 ture is a dictionary between representation-theoretic\nproperties of the a
 rchimedean component \\pi_{\\infty}\, e.g.\n"non-degenerate or degenerate 
 limit of discrete series" (LDS)\, and\ngeometric properties of \\pi\, e.g.
  "appears in the coherent cohomology\nof a Shimura variety or Griffiths-Sc
 hmid manifold".\n\nWe propose a systematic study of the conjectural implic
 ations of\nLanglands functoriality to the above conjecture. To this end\, 
 we study\nthe (in)variance of the dichotomies "LDS/non-LDS" and\n"non-dege
 nerate/degenerate" under functoriality. In the positive\ndirection\, we gi
 ve examples where functoriality implies new cases of\nalgebraicity and (wo
 rk in progress) show that one class of these\nfollows unconditionally from
  Arthur's work on endoscopy.
LOCATION:MR13
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