Extensions in the cohomology of Hilbert modular varieties

Cosmin Davidescu, Anthony J. Scholl

Published 2020-03-17Version 1

We describe extension classes arising in the $\ell$-adic and Hodge cohomology of Hilbert modular varieties, generalising results of Caspar to arbitrary dimensions. We show that this description is consistent with the "plectic conjectures" of Nekov\'a\v{r} and the second author.