Hodge completed derived de Rham algebra of a perfect ring

2019/01/08 by Davide Marangoni, Marangoni, Davide
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1901.02365

openalex publication_date 2019/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Derived de Rham cohomology has been recently used in several contexts, as in works of Beilinson and Bhatt on p-adic periods morphisms and Morin on numerical invariants for special values of zeta functions. Inspired by some results of Morin, we aimed to compute Hodge completed derived de Rham complex in the case of a rings map ℤ\longrightarrow k, factoring through \mathbbF_p, with k a perfect ring (i.e. the Frobenius map is an automorphism).

Related

• Completions and derived de Rham cohomology
• p-adic derived de Rham cohomology
• Dwork cohomology, de Rham cohomology, and hypergeometric functions
• de Rham Cohomology of Period Domains
• Milne's correcting factor and derived de Rham cohomology