The Weak Leopoldt Conjecture for adjoint representations

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• Patrick Allen (University of Illinois at Urbana-Champaign)
• Tuesday 23 May 2017, 14:30-15:30
• MR13.

If you have a question about this talk, please contact G. Rosso.

For a given number field F and a prime p, one of the many equivalent formulations of Leopoldt’s conjecture is that the second Galois cohomology group of F with coefficients in the trivial p-adic representation vanishes. Almost all progress on Leopoldt’s conjecture has come via transcendental 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 Galois representations V, and a precise formulation of this question this is known as the Weak Leopoldt Conjecture for V. Under certain assumptions, we show that the Weak Leopoldt Conjecture holds for the adjoint representation 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.

This talk is part of the Number Theory Seminar series.

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