Partial Hasse invariants on splitting models of Hilbert modular varieties. (Invariants de Hasse partiels sur les modèles de décomposition des variétés de Hilbert modulaires.) (English. French summary) Zbl 1430.11061

Reduzzi, Davide A.; Xiao, Liang

Ann. Sci. Éc. Norm. Supér. (4) 50, No. 3, 579-607 (2017).

Summary: Let \(F\) be a totally real field of degree \(g\), and let \(p\) be a prime number. We construct \(g\) partial Hasse invariants on the characteristic \(p\) fiber of the Pappas-Rapoport splitting model of the Hilbert modular variety for \(F\) with level prime to \(p\), extending the usual partial Hasse invariants defined over the Rapoport locus. In particular, when \(p\) ramifies in \(F\), we solve the problem of lack of partial Hasse invariants. Using the stratification induced by these generalized partial Hasse invariants on the splitting model, we prove in complete generality the existence of Galois pseudo-representations attached to Hecke eigenclasses of paritious weight occurring in the coherent cohomology of Hilbert modular varieties \(\mod p^m\), extending a previous result of M. Emerton and the authors which required \(p\) to be unramified in \(F\).

MSC:

11F41	Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
14G35	Modular and Shimura varieties
11G18	Arithmetic aspects of modular and Shimura varieties
11F80	Galois representations

Keywords:

partial Hasse invariants; Pappas-Rapoport splitting models; Hilbert modular forms; Galois representations