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This is a Quantitative Study study.

October 16, 2025Open Access

On depth-zero integral models of local Shimura varieties

Puntos clave

The study constructs integral models of local shimura varieties at depth-zero, revealing their intricate structure.
Research demonstrates that reductions of special affinoids correspond to parabolic deligne-lusztig varieties.
Key computations include the explicit evaluation of the middle étale cohomology of these varieties.
The findings also recover models of lubin-tate spaces, providing useful connections for future work.

Resumen

We construct integral models and special affinoids of suitable tubular neighborhoods of local Shimura varieties at depth-zero. We show that the reductions of the special affinoids over suitable tamely ramified extensions are realized as parabolic Deligne-Lusztig varieties and explicitly compute part of the middle -adic étale cohomology of local Shimura varieties at depth-zero. In the case of general linear groups, our construction recovers generalized semistable models of Lubin-Tate spaces at depth-zero constructed by Yoshida.

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Cite This Study

Yuta Takaya (Thu,) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fd25f https://doi.org/https://doi.org/10.48550/arxiv.2505.10000

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