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Ausoni–Bökstedt duality for topological Hochschild homology
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Greenlees, John (2016) Ausoni–Bökstedt duality for topological Hochschild homology. Journal of Pure and Applied Algebra, 220 (4). pp. 1382-1402. doi:10.1016/j.jpaa.2015.09.007 ISSN 0022-4049.
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Official URL: https://doi.org/10.1016/j.jpaa.2015.09.007
Abstract
We consider the Gorenstein condition for topological Hochschild homology, and show that it holds remarkably often. More precisely, if R is a commutative ring spectrum and R −→ k is a map to a field of characteristic p then, provided k is small as an R-module, T HH(R; k) is Gorenstein in the sense of [11]. In particular, this holds if R is a (conventional) regular local ring with residue field k of characteristic p. Using only B¨okstedt’s calculation of T HH(k), this gives a non-calculational proof of dualities observed by B¨okstedt [9] and Ausoni [3], Lindenstrauss-Madsen [17], AngeltweitRognes [4] and others.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Homology theory, Cohomology operations, Gorenstein rings | ||||||
Journal or Publication Title: | Journal of Pure and Applied Algebra | ||||||
Publisher: | Elsevier Science BV | ||||||
ISSN: | 0022-4049 | ||||||
Official Date: | April 2016 | ||||||
Dates: |
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Volume: | 220 | ||||||
Number: | 4 | ||||||
Page Range: | pp. 1382-1402 | ||||||
DOI: | 10.1016/j.jpaa.2015.09.007 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 20 March 2018 | ||||||
Date of first compliant Open Access: | 21 March 2018 |
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