Number Theory Seminar

Harris-Lan-Taylor-Thorne and Scholze construct Galois representations associated to regular algebraic, cuspidal automorphic representations and to torsion classes in the cohomology of locally symmetric spaces for GL_n over a CM field. In the case of a totally real field, these Galois representations are expected to be odd, in a sense we will make precise. We make use of Scholze's p-adic interpolation techniques to prove this expectation. This is joint work with Bao Le Hung.