Ausoni-Bökstedt duality for topological Hochschild homology

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• 作者：J.P.C. Greenlees ^{j.greenlees@sheffield.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：220
• 期：4
• 页码：1382-1402
• 全文大小：472 K

文摘

We consider the Gorenstein condition for topological Hochschild homology, and show that it holds remarkably often [7]. More precisely, if R   is a commutative ring spectrum and R⟶k$R⟶k$ is a map to a field of characteristic p then, provided k is small as an R  -module, THH(R;k)$THH(R;k)$ 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 Bökstedt's calculation of 65b050db1e7bb210c0cd" title="Click to view the MathML source">THH(k)$THH(k)$, this gives a non-calculational proof of dualities visible in calculations of Bökstedt [9], Ausoni [3], Lindenstrauss and Madsen [17], Angeltveit and Rognes [2] and others.