Bökstedt periodicity and quotients of DVRs

2022/08/01 by Achim Krause, Thomas Nikolaus · 3 citations
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #Algebraic structures and combinatorial models

paper · pdf · doi:10.1112/s0010437x22007655

Abstract

In this paper we compute the topological Hochschild homology of quotients of discrete valuation rings (DVRs). Along the way we give a short argument for Bökstedt periodicity and generalizations over various other bases. Our strategy also gives a very efficient way to redo the computations of \operatorname THH (respectively, logarithmic \operatorname THH ) of complete DVRs originally due to Lindenstrauss and Madsen (respectively, Hesselholt and Madsen).

Citations

• On the structure and ideal theory of complete local rings
• On topological cyclic homology

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