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This is a Quantitative Study study.

October 16, 2025Open Access

Locally analytic vectors in the completed cohomology of unitary Shimura curves

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Authors

QTQiu TianUniversity of Alabama BSBuchin SuYunnan Normal University

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Implication

Analysis demonstrates classicality of Galois representations in the context of unitary Shimura curves, indicating significant applications in p-adic representation theory.

Key Points

The study reveals classicality results regarding two-dimensional Galois representations in locally analytic vectors.
It establishes that certain two-dimensional representations appearing in completed cohomology are σ-de Rham.
Methods are developed using Lue Pan’s approach to explore locally analytic vectors in this mathematical context.
The findings have broader implications for the p-adic local Langlands program and coherent cohomology.

Cite This Study

Tian et al. (2025) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fd3a4 https://doi.org/10.48550/arxiv.2505.10290

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Implication

Analysis demonstrates classicality of Galois representations in the context of unitary Shimura curves, indicating significant applications in p-adic representation theory.

Locally analytic vectors in the completed cohomology of unitary Shimura curves

Discussion

Member takes

Implication

Key Points

Cite This Study

Locally analytic vectors in the completed cohomology of unitary Shimura curves

Discussion

Member takes

Implication

Key Points

Cite This Study

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