Frobenius height of prismatic cohomology with coefficients
Haoyang Guo, Shizhang Li
公開日: 2023/9/13
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.