Frobenius height of prismatic cohomology with coefficients
Algebraic Geometry
2025-09-15 v2 Number Theory
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.
Keywords
Cite
@article{arxiv.2309.06663,
title = {Frobenius height of prismatic cohomology with coefficients},
author = {Haoyang Guo and Shizhang Li},
journal= {arXiv preprint arXiv:2309.06663},
year = {2025}
}
Comments
v1: 42 pages; v2: 52 pages, we added a section discussing necessary homological algebras in graded or filtered settings, comments welcome