A note on higher almost ring theory

2024/09/03 by Fabian Hebestreit, Peter Scholze, Hebestreit, Fabian +1
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2409.01940

openalex publication_date 2024/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explain a derived version of the basic construction of localisations of module categories by means of idempotent ideals, which lie at the heart of Faltings' almost ring theory. We use it to provide an example of a commutative algebra in positive characteristic whose Frobenius endomorphism does not induce an isomorphism on its smashing spectrum.

Related

• Almost ring theory
• Almost Noetherian rings and modules
• Almost Gorenstein rings
• Almost mathematics of pointed symmetric monoidal model categories by Smith ideal theory
• D-module generation in positive characteristic via Frobenius descent