Hilbert modular forms and p-adic Hodge theory

Abstract

We consider the p-adic Galois representation associated to a Hilbert modular form. We show the compatibility with the local Langlands correspondence at a place divising p under a certain assumption. We also prove the monodromy-weight conjecture. The prime-to-p case is established by Carayol.

45 pages: page size adjusted

Cited by in corpus (27)

• Formes modulaires de Hilbert modulo p et valeurs d'extensions galoisiennes
• p-adic Cohomology and classicality of overconvergent Hilbert modular forms
• Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence
• The universal $p$-adic Gross-Zagier formula
• On 2-dimensional 2-adic Galois representations of local and global fields
• Modularity of nearly ordinary 2-adic residually dihedral Galois representations
• On Goren-Oort stratification for quaternionic Shimura varieties
• Level optimization in the totally real case
• On the modularity of 2-adic potentially semi-stable deformation rings
• On Serre's modularity conjecture for 2-dimensional mod p representations of G_Q unramified outside p
• Overconvergent relative de Rham cohomology over the Fargues-Fontaine curve
• $\mathcal{L}$-invariants and logarithm derivatives of eigenvalues of Frobenius
• Big principal series, p-adic families and L-invariants
• On the quantitative variation of congruence ideals and integral periods of modular forms
• On some partially de Rham Galois representations
• A $p$-adic adjoint $L$-function and the ramification locus of the Hilbert modular eigenvariety
• $\mathcal{L}$-invariants, partially de Rham families and local-global compatibility
• $\mathcal{L}$-invariants and local-global compatibility for the group ${\mathrm{GL}}_2/F$
• Indivisibility of Heegner cycles over Shimura curves and Selmer groups
• Unramifiedness of weight one Hilbert Hecke algebras
• On symmetric power L-invariants of Iwahori level Hilbert modular forms
• Heights of CM cycles and derivatives of L-series
• Cohomology of $(\phi ,\Gamma )$-modules over pseudorigid spaces
• L-invariants for Hilbert modular forms
• The Chabauty-Kim Method for Relative Completions
• Ramification of Hilbert eigenvarieties at classical points
• Hirzebruch-Zagier classes and rational elliptic curves over quintic fields