# Derived invariants from topological Hochschild homology

## TL;DR

This paper investigates derived invariants of algebraic varieties in positive characteristic derived from topological Hochschild homology, revealing new restrictions on Hodge numbers and extending prior results to this setting.

## Contribution

It introduces new derived invariants from topological Hochschild homology and studies their behavior under derived equivalences in positive characteristic.

## Key findings

- Derived invariants are preserved under derived equivalences.
- Restrictions on Hodge numbers for derived equivalent varieties in positive characteristic.
- Extension of previous results to the setting of positive characteristic.

## 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.