2004/11/07 by Mladen Dimitrov, Dimitrov, Mladen · 1 citation
Mathematics · #11F33 #11F41 #11F67 #11F80 #14F05 #14F40 #14G35 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.math/0411152
openalex publication_date 2004/11/07 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28
The aim of this paper is to extend some arithmetic results on elliptic\nmodular forms to the case of Hilbert modular forms. Among these results let's\nmention : (1) the control of the image of the Galois representation modulo p,\n(2) Hida's congruence criterion outside an explicit set of primes p, and (3)\nthe freeness of the integral cohomology of the Hilbert modular variety over\ncertain local components of the Hecke algebra and the Gorenstein property of\nthese local algebras.\n We study the arithmetic of the Hilbert modular forms by studying their modulo\np Galois representations and our main tool is the action of the inertia\ngroups at the primes above p. In order to determine this action, we compute\nthe Hodge-Tate (resp. the Fontaine-Laffaille) weights of the p-adic (resp.\nthe modulo p) etale cohomology of the\n Hilbert modular variety. The cohomological part of our paper is inspired by\nthe work of Mokrane, Polo and Tilouine on the cohomology of the Siegel modular\nvarieties and builds upon the geometric constructions of math.NT/0212071 and\nmath.NT/0212072.\n