Comparing cyclotomic structures on different models for topological Hochschild homology

被引：5

作者：

Dotto, Emanuele ^{[1
]}

Malkiewich, Cary ^{[2
]}

Patchkoria, Irakli ^{[3
]}

Sagave, Steffen ^{[4
]}

Woo, Calvin ^{[5
]}

机构：

[1] Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany

[2] SUNY Binghamton, Dept Math, POB 6000, Binghamton, NY 13902 USA

[3] Univ Aberdeen, Dept Math, Fraser Noble Bldg, Aberdeen AB24 3UE, Scotland

[4] Radboud Univ Nijmegen, IMAPP, POB 9010, NL-6500 GL Nijmegen, Netherlands

[5] Indiana Univ, Dept Math, 831 E 3rd St, Bloomington, IN 47405 USA

来源：

JOURNAL OF TOPOLOGY | 2019年 / 12卷 / 04期

基金：

新加坡国家研究基金会;

关键词：

ALGEBRAIC K-THEORY; SYMMETRIC SPECTRA; HOMOTOPY-THEORY; TRACE;

D O I：

10.1112/topo.12116

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The topological Hochschild homology THH(A) of an orthogonal ring spectrum A can be defined by evaluating the cyclic bar construction on A or by applying Bokstedt's original definition of THH to A. In this paper, we construct a chain of stable equivalences of cyclotomic spectra comparing these two models for THH(A). This implies that the two versions of topological cyclic homology resulting from these variants of THH(A) are equivalent.

引用

页码：1146 / 1173

页数：28

共 15 条

[1] Real topological Hochschild homology
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[2] Localization theorems in topological Hochschild homology and topological cyclic homology
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[6] The Segal conjecture for topological Hochschild homology of complex cobordism
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[9] Detecting periodic elements in higher topological Hochschild homology
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[10] Generalized spectral categories, topological Hochschild homology and trace maps
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