paper

A note on higher almost ring theory

arXiv:2409.01940

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.

13 pages, v2: added further examples and discussion of Smith ideals

A note on higher almost ring theory · wovepaper