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arXiv · 2109.02854

Twisted Equivalences in Spectral Algebraic Geometry

Chang-Yeon Chough
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Abstract

We study twisted derived equivalences for schemes in the setting of spectral algebraic geometry. To this end, we introduce the notion of a twisted equivalence and show that a twisted equivalence for perfect spectral algebraic stacks admitting a quasi-finite presentation supplies an equivalence between the stacks, which compensate for the failure of twisted derived equivalences for non-affine schemes to provide an isomorphism of the schemes. In the case of (not necessarily connective) commutative ring spectra, we also prove a spectral analogue of Rickard's theorem, which shows that a derived equivalence of associative rings induces an isomorphism between their centers.

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Chang-Yeon Chough. 2021-09-07. Twisted Equivalences in Spectral Algebraic Geometry. https://arxiv.org/abs/2109.02854

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