Mod $p$ sheaves on Witt flags

Robert Cass; João Lourenço

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arXiv · 2503.01796

Mod $p$ sheaves on Witt flags

Robert Cass·João Lourenço

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Abstract

We characterize Cohen--Macaulay and $\varphi$-rational perfect schemes in terms of their perverse \'etale mod $p$ sheaves. Using inversion of adjunction, we prove that sufficiently small Schubert varieties in the Witt affine flag variety are perfections of globally $+$-regular varieties, and hence they are $\varphi$-rational. Our methods apply uniformly to all affine Schubert varieties in equicharacteristic, as well as classical Schubert varieties, thereby answering a question of Bhatt. As a corollary, we deduce that scheme-theoretic local models always have $\varphi$-split special fiber.

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BibTeX RIS

Robert Cass, João Lourenço. 2025-03-03. Mod $p$ sheaves on Witt flags. https://arxiv.org/abs/2503.01796

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