Vol. 6, No. 3, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN: 2379-1691 (e-only)
ISSN: 2379-1683 (print)
 
Author index
To appear
 
Other MSP journals
This article is available for purchase or by subscription. See below.
A multiplicative comparison of Mac Lane homology and topological Hochschild homology

Geoffroy Horel and Maxime Ramzi

Vol. 6 (2021), No. 3, 571–605
Abstract

Let Q denote Mac Lane’s Q-construction and the smash product of spectra. We construct an equivalence Q(R) R in the category of A ring spectra for any ring R, thus proving a conjecture of Fiedorowicz, Pirashvili, Schwänzl, Vogt and Waldhausen. More precisely, we construct a symmetric monoidal structure on Q (in the -categorical sense) extending the usual monoidal structure, for which we prove an equivalence Q() as symmetric monoidal functors. From this, we obtain a new proof of the equivalence HML(R,M) THH(R,M) originally proved by Pirashvili and Waldhausen. This equivalence is in fact made symmetric monoidal, and so it also provides a proof of the equivalence HML(R) THH(R) as E ring spectra, when R is a commutative ring.

PDF Access Denied

We have not been able to recognize your IP address 44.222.64.76 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
Mac Lane homology, Hochschild homology, topological Hochschild homology, $Q$-construction
Mathematical Subject Classification
Primary: 19D55
Secondary: 18G99
Milestones
Received: 12 December 2020
Revised: 14 January 2021
Accepted: 4 February 2021
Published: 11 September 2021
Authors
Geoffroy Horel
Université Sorbonne Paris Nord
Villetaneuse
France
Maxime Ramzi
Department of Mathematical Sciences
University of Copenhagen
Denmark
École Normale Supérieure
Paris
France