Ausoni-Bökstedt duality for topological Hochschild homology
Ausoni-Bökstedt duality for topological Hochschild homology
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拓扑 Hochschild 同调的 Ausoni-Bökstedt 对偶性
DOI：
10.1016/j.jpaa.2015.09.007
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发表时间：
2016
影响因子：
0.8
通讯作者：
Greenlees J
中科院分区：
文献类型：
--
作者：
Greenlees J
我们考虑了拓扑Hochschild同调的Gorenstein条件，并证明了它经常成立[7]。更确切地说，如果R是交换环谱，且R⟶k是到特征为p的域的映射，则如果k是小的R-模，则TH H(R；k)在[11]的意义下是Gorenstein的。特别地，如果R是具有特征p的剩余域k的(常规)正则局部环，则这是成立的。仅使用Bökstedt对T H H(K)的计算，这给出了在Bökstedt[9]、Ausoni[3]、Lindenstrauss和Madsen[17]、Angeltveit和Rognes[2]等人的计算中可见的对偶性的非计算证明。
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 is a map to a field of characteristic p then, provided k is small as an R-module, T H H (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 T H H (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.