Modular forms of weight one, motivic cohomology and the Jacquet-Langlands correspondence

by Prof. Kartik Prasanna (University of Michigan, Ann Arbor)

Tuesday 27 Dec 2022, 16:00 → 17:00 Asia/Kolkata

AG-77

Abstract: I will discuss some joint work (in progress) with Ichino. In previous work, we showed that the Jacquet-Langlands correspondence for cohomological Hilbert modular forms preserves rational Hodge structures, as predicted by the Tate conjecture. In this talk, I will discuss a related result in the case of weight one forms, which are non-cohomological. In this case, the Tate conjecture does not apply and thus it is not obvious what the content of such a result should be. I will motivate and explain the statement, which is suggested by another recent development, namely the conjectural connection between motivic cohomology and the cohomology of locally symmetric spaces.