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Frobenius height of prismatic cohomology with coefficients

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arxiv 2309.06663 v2 pith:4O7TX4TZ submitted 2023-09-13 math.AG math.NT

Haoyang Guo , Shizhang Li This is my paper · ORCID
classification math.AGmath.NT
keywords frobeniusprismaticheightbehaviorbhatt--luriecoefficientscohomologycrucially
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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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Cited by 2 Pith papers

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  1. A Dieudonn\'e theory for analytic p-divisible groups and applications to Shimura varieties

    math.AG 2026-02 conditional novelty 8.0 of 10

    Analytic p-divisible groups over good adic spaces are equivalent to Hodge-Tate triples (T_pG, Lie G, f_G), and dualizable ones to minuscule local shtukas — yielding moduli descriptions of EL/PEL local Shimura varieties.

  2. Perfect $F$-gauges and finite flat group schemes

    math.NT 2025-09 conditional novelty 7.0 of 10

    Over arbitrary p-adic formal bases, finite locally free p-power torsion commutative group schemes are exactly the perfect F-gauges of Tor amplitude [-1,0] and Hodge-Tate weights 0,1, via an exact, Cartier-duality-comp...

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