A note on higher almost ring theory
Commutative Algebra
2025-10-28 v2 Algebraic Topology
Number Theory
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.
Cite
@article{arxiv.2409.01940,
title = {A note on higher almost ring theory},
author = {Fabian Hebestreit and Peter Scholze},
journal= {arXiv preprint arXiv:2409.01940},
year = {2025}
}
Comments
13 pages, v2: added further examples and discussion of Smith ideals