2015/01/27 by Yiwen Ding, Ding, Yiwen
Mathematics · #11F #11S #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1501.06901
openalex publication_date 2015/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F be a totally real number field, \wp a place of F above p. Let ρ be a 2-dimensional p-adic representation of Gal(F/F) which appears in the étale cohomology of quaternion Shimura curves (thus ρ is associated to Hilbert eigenforms). When the restriction ρ\wp:=ρ|_D\wp at the decomposition group of \wp is semi-stable non-crystalline, one can associate to ρ\wp the so-called Fontaine-Mazur L-invariants, which are however invisible in the classical local Langlands correspondence. In this paper, we prove one can find these L-invariants in the completed cohomology group of quaternion Shimura curves, which generalizes some of Breuil's results in GL2/ℚ-case.