A note on higher almost ring theory

Fabian Hebestreit; Peter Scholze

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arXiv · 2409.01940

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.

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Fabian Hebestreit, Peter Scholze. 2024-09-03. A note on higher almost ring theory. https://arxiv.org/abs/2409.01940

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