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arXiv · 1906.12267

Derived invariants from topological Hochschild homology

Benjamin Antieau·Daniel Bragg
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Abstract

We consider derived invariants of varieties in positive characteristic arising from topological Hochschild homology. Using theory developed by Ekedahl and Illusie-Raynaud in their study of the slope spectral sequence, we examine the behavior under derived equivalences of various $p$-adic quantities related to Hodge-Witt and crystalline cohomology groups, including slope numbers, domino numbers, and Hodge-Witt numbers. As a consequence, we obtain restrictions on the Hodge numbers of derived equivalent varieties, partially extending results of Popa-Schell to positive characteristic.

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Benjamin Antieau, Daniel Bragg. 2019-06-28. Derived invariants from topological Hochschild homology. https://arxiv.org/abs/1906.12267

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