RTG Seminar on Number Theory Seminar

A surprising property of cohomology of symmetric spaces is that Hecke operators can act on multiple cohomological degrees with the same eigenvalues. We will discuss this phenomenon for 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. This extends the conjectures of Venkatesh, Prasanna, and Harris to Hilbert modular varieties. Speaker(s): Alex Horawa (UM)