Two monoidal structures on Satake category in mixed characteristic

Katsuyuki Bando

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arXiv · 2302.07376

Two monoidal structures on Satake category in mixed characteristic

Katsuyuki Bando

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Abstract

Fargues and Scholze proved the geometric Satake equivalence over the Fargues-Fontaine curve. This can be transferred to the geometric Satake equivalence concerning a Witt vector affine Grassmannian via nearby cycle. On the other hand, Zhu proved the geometric Satake equivalence concerning a Witt vector affine Grassmannian. In this paper, we explain the coincidence of these two geometric Satake equivalences, including the coincidence of the two symmetric monoidal structures on the Satake category.

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Katsuyuki Bando. 2023-02-14. Two monoidal structures on Satake category in mixed characteristic. https://arxiv.org/abs/2302.07376

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