Bökstedt periodicity and quotients of DVRs

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 $\opera...

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Bibliographic Details
Published in:Compositio mathematica 2022-08, Vol.158 (8), p.1683-1712
Main Authors: Krause, Achim, Nikolaus, Thomas
Format: Article
Language:English
Subjects:
Algebra
Homology
Quotients
Rings (mathematics)
Valuation
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Summary: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).
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X22007655