The strong K\"unneth theorem for topological periodic cyclic homology

TL;DR

This paper establishes a strong K"unneth theorem for topological periodic cyclic homology, enhancing understanding of its monoidal properties in the context of smooth and proper dg categories over finite fields.

Contribution

It proves a strong K"unneth theorem for topological periodic cyclic homology, demonstrating its monoidal behavior for certain dg categories over perfect fields.

Findings

Topological periodic cyclic homology is a strong symmetric monoidal functor.

The theorem applies to smooth and proper dg categories over perfect fields.

Enhances the theoretical framework of cyclic homology in algebraic geometry.

Abstract

Topological periodic cyclic homology (i.e., $\mathbb{T}$-Tate fixed points of $THH$) has the structure of a strong symmetric monoidal functor of smooth and proper dg categories over a perfect field of finite characteristic.