Motivic action on coherent cohomology of Hilbert modular varieties

Aleksander Horawa, University of Michigan
IAS - Simonyi Hall Seminar Room SH-101

In-Person and Online Talk 

Zoom link:

Passcode: The three digit integer that is the cube of the sum of its digits

A surprising property of the cohomology of locally symmetric spaces is that Hecke operators can act on multiple cohomological degrees with the same eigenvalues. We will discuss this phenomenon for the coherent cohomology of line bundles on modular curves and, more generally, Hilbert modular varieties. We propose an arithmetic explanation: a hidden degree-shifting action of a certain motivic cohomology group (the Stark unit group). This extends the conjectures of Venkatesh, Prasanna, and Harris to Hilbert modular varieties.