Arithmetic Breuil-Kisin-Fargues modules and comparison of integral p-adic Hodge theories

2019/10/07 by Du Heng, Du, Heng
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1910.02939

openalex publication_date 2019/10/07 · openalex created_date 2023/02/15 · openalex updated_date 2026/07/28

Abstract

Let K be a discrete valuation field with perfect residue field, we study the functor from weakly admissible filtered (φ,N,G_K)-modules over K to the isogeny category of Breuil-Kisin-Fargues G_K-modules. This functor is the composition of a functor defined by Fargues-Fontaine from weakly admissible filtered (φ,N,G_K)-modules to G_K-equivariant modifications of vector bundles over the Fargues-Fontaine curve X_FF, with the functor of Fargues-Scholze that between the category of admissible modifications of vector bundles over X_FF and the isogeny category of Breuil-Kisin-Fargues modules. We study those objects appear in the essential image of the above functor and call them arithmetic BKF modules. We show certain rigidity result of arithmetic BKF modules and use it to compare existing p-adic Hodge theories at A_inf level.

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