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arXiv · 2309.06663

Frobenius height of prismatic cohomology with coefficients

Haoyang Guo·Shizhang Li
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Abstract

We study the behavior of Frobenius operators on smooth proper pushforwards of prismatic F-crystals. In particular we show that the i-th pushforward has its Frobenius height increased by at most i. Our proof crucially uses the notion of prismatic F-gauges introduced by Drinfeld and Bhatt--Lurie and its relative version, and we give a self-contained treatment without using the stacky formulation.

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Haoyang Guo, Shizhang Li. 2023-09-13. Frobenius height of prismatic cohomology with coefficients. https://arxiv.org/abs/2309.06663

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