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arXiv:2409.01940math.AC

A note on higher almost ring theory

Fabian Hebestreit, Peter Scholze

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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.

arXiv comments
13 pages, v2: added further examples and discussion of Smith ideals
Journal reference
DOI
Subjects
math.ACCommutative Algebra math.ATAlgebraic Topology math.NTNumber Theory

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  1. Mathematics is hard for mathematicians to understand too 1 comment

    • > I understand that some degree of formalism is required to enable the sharing of knowledge amongst people across a variety of languages, but sometimes I'll read a white paper and think "wow, this could be written a LOT more simply". OK, challenge accepted: find a way to write…

      aleph_minus_oneView on HNParent context

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