Volume 8, issue 1 (2004)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23, 1 issue

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
Formal groups and stable homotopy of commutative rings

Stefan Schwede

Geometry & Topology 8 (2004) 335–412

arXiv: math.AT/0402372


We explain a new relationship between formal group laws and ring spectra in stable homotopy theory. We study a ring spectrum denoted DB which depends on a commutative ring B and is closely related to the topological André–Quillen homology of B. We present an explicit construction which to every 1–dimensional and commutative formal group law F over B associates a morphism of ring spectra F: H DB from the Eilenberg–MacLane ring spectrum of the integers. We show that formal group laws account for all such ring spectrum maps, and we identify the space of ring spectrum maps between H and DB. That description involves formal group law data and the homotopy units of the ring spectrum DB.

ring spectrum, formal group law, André–Quillen homology
Mathematical Subject Classification 2000
Primary: 55U35
Secondary: 14L05
Forward citations
Received: 12 July 2003
Revised: 12 February 2004
Accepted: 30 January 2004
Published: 14 February 2004
Proposed: Bill Dwyer
Seconded: Thomas Goodwillie, Haynes Miller
Stefan Schwede
Mathematisches Institut
Universität Bonn
53115 Bonn