Let F/F_0 be a quadratic extension of non-archimedean local fields of residue characteristic p different from 2. Let R be an algebraically closed field of characteristic different from p. For pi a supercuspidal representation of G=GLn(F) over R and H a unitary group in n variables contained in G, we prove that pi is distinguished by H if and only if pi is Galois invariant. When R is the complex field and F is a p-adic field, this result first as a conjecture proposed by Jacquet was proved in 2010’s by Feigon-Lapid-Offen by using global method. In this talk, I will explain how to give a local proof which works for our case in general. Moreover we further study the dimension of distinction and show that it is at most one.
L’exposé sera retransmis via zoom.
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