2014/05/24 by Davide A. Reduzzi, Liang Xiao, Reduzzi, Davide A. +1
Mathematics · #11F41 (primary) 14G35 11G18 11F80 (secondary) #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Cohomology #Combinatorics #Discrete mathematics #FOS: Mathematics #Galois module #Mathematics #Modular form #Number Theory (math.NT) #Prime (order theory) #Pure mathematics #Shimura variety #math.NT #msc:11F41 #msc:11F80 #msc:11G18 #msc:14G35
paper · pdf · doi:10.48550/arxiv.1405.6349
24 pages, refereed version, index changed from the previous version
openalex publication_date 2014/05/24 · arxiv created 2016/03/02 · arxiv updated 2016/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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 pm, extending a previous result of M. Emerton and the authors which required p to be unramified in F.