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Bhavithry Sen Puliparambil

doi:10.3390/biology11101495

On locally analytic vectors of the completed cohomology of modular curves II

2026-01-01

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Lue Pan *

DOI：10.4007/annals.2026.203.1.3

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This is a continuation of our previous work on the locally analytic vectors of the completed cohomology of modular curves. We construct differential operators on modular curves with infinite level at p in both holomorphic and anti-holomorphic directions. As applications, we reprove a classicality result of Emerton which says that every absolutely irreducible two dimensional Galois representation that is regular de Rham at p and appears in the completed cohomology of modular curves comes from an eigenform. Moreover, we give a geometric description of the locally analytic representations of GL2(Qp) attached to such a Galois representation in the completed cohomology.

Keywords:

Fontaine-Mazur conjecture

completed cohomology

p-adic local Langlands

Fontaine operator

On locally analytic vectors of the completed cohomology of modular curves II

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