On locally analytic vectors of the completed cohomology of modular curves

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Abstract

We study the locally analytic vectors in the completed cohomology of modular curves and determine the eigenvectors of a rational Borel subalgebra of. As applications, we prove a classicality result for overconvergent eigenforms of weight 1 and give a new proof of the Fontaine-Mazur conjecture in the irregular case under some mild hypotheses. For an overconvergent eigenform of weight k, we show its corresponding Galois representation has Hodge-Tate-Sen weights and prove a converse result.

Original languageEnglish (US)
Article numbere7
JournalForum of Mathematics, Pi
Volume10
DOIs
StatePublished - Mar 7 2022

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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