Relative (φ,Γ)-modules and prismatic F-crystals

2021/10/12 by Yu Min, Yupeng Wang, Min, Yu +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2110.06076

openalex publication_date 2021/10/12 · openalex created_date 2021/10/25 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that for any p-adic smooth separated formal scheme \mathfrak X, the category of prismatic F-crystals with I inverted is equivalent to the category of étale \mathbb Z_p-local systems on the generic fiber of \mathfrak X. We also compare the cohomology of the corresponding coefficients.

Related

• Completed prismatic F-crystals and crystalline Z_p-local systems
• A prismatic approach to crystalline local systems
• A note on étale (φ,Γ)-modules in families
• Prismatic F-crystals and Lubin-Tate (φ_q,Γ)-modules
• A prismatic approach to (φ, G)-modules and F-crystals