On locally analytic vectors of the completed cohomology of modular curves

Lue Pan

doi:10.1017/fmp.2022.1

On locally analytic vectors of the completed cohomology of modular curves

Lue Pan

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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 language	English (US)
Article number	e7
Journal	Forum of Mathematics, Pi
Volume	10
DOIs	https://doi.org/10.1017/fmp.2022.1
State	Published - 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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10.1017/fmp.2022.1

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On locally analytic vectors of the completed cohomology of modular curves

Abstract

All Science Journal Classification (ASJC) codes

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