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SUMMARY:The Weak Leopoldt Conjecture for adjoint representations - Patrick
  Allen (University of Illinois at Urbana-Champaign)
DTSTART:20170523T133000Z
DTEND:20170523T143000Z
UID:TALK72370@talks.cam.ac.uk
CONTACT:G. Rosso
DESCRIPTION:For a given number field F and a prime p\, one of the many equ
 ivalent formulations of Leopoldt's conjecture is that the second Galois co
 homology group of F with coefficients in the trivial p-adic representation
  vanishes. Almost all progress on Leopoldt's conjecture has come via trans
 cendental methods\, with one notable exception being Iwasawa's result that
  the dimension of this cohomology group remains bounded up the cyclotomic 
 tower. One can ask if similar phenomena holds for more general p-adic Galo
 is representations V\, and a precise formulation of this question this is 
 known as the Weak Leopoldt Conjecture for V. Under certain assumptions\, w
 e show that the Weak Leopoldt Conjecture holds for the adjoint representat
 ion of the p-adic Galois representation associated to a regular algebraic 
 cuspidal automorphic representation of GLn over a CM field. This is joint 
 work with Chandrashekhar Khare.
LOCATION:MR13
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