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arXiv · 2505.01204

Transitivity of the $\mathbb{B}^+_\mathrm{dR}$-loop group action on Schubert cells

Sean Howe
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Abstract

For $G$ a connected linear algebraic group over a $p$-adic field, we show that the action of $G(\mathbb{B}^+_{\mathrm{dR}})$ on each Schubert cell in the $\mathbb{B}_{\mathrm{dR}}^+$-affine Grassmannian is transitive in the étale topology on affinoid perfectoids, generalizing a result in the reductive case due to Fargues and Scholze.

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Sean Howe. 2026-02-05. Transitivity of the $\mathbb{B}^+_\mathrm{dR}$-loop group action on Schubert cells. https://arxiv.org/abs/2505.01204

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