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Short talk: Motivic action conjectures

Posted in
Alexander Horawa
University of Oxford
Mon, 06/03/2023 - 15:00 - 15:15
MPIM Lecture Hall

A surprising property of the cohomology of locally symmetric spaces is that Hecke operators can act on multiple cohomological degrees with the same eigenvalues. A recent series of conjectures proposes an arithmetic explanation: a hidden degree-shifting action of a certain motivic cohomology group. We will give an overview of these conjectures, focusing on the examples of $GL_2$ over Q and over quadratic fields, and $GSp_4$ over Q.

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