On the Blumberg-Mandell Künneth theorem for TP

2017/10/16 by Benjamin Antieau, Akhil Mathew, Antieau, Benjamin +3
Mathematics · Medicine · #14F30 #16E40 #19D55 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1710.05658

openalex publication_date 2017/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a new proof of the recent Künneth theorem for periodic topological cyclic homology (TP) of smooth and proper dg categories over perfect fields of characteristic p>0 due to Blumberg and Mandell. Our result is slightly stronger and implies a finiteness theorem for topological cyclic homology (TC) of such categories.

Related

• The strong Künneth theorem for topological periodic cyclic homology
• On the periodic topological cyclic homology of DG categories in characteristic p
• On a Hodge theoretic property of the Kuenneth map in periodic cyclic homology
• Nilpotent invariance of semi-topological K-theory of dg-algebras and the lattice conjecture
• Topological cyclic homology