Geometry & Topology, Vol. 8 (2004) Paper no. 9, pages 335--412.

Formal groups and stable homotopy of commutative rings

Stefan Schwede

Abstract. 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 Andre-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_*: HZ --> 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 HZ and DB. That description involves formal group law data and the homotopy units of the ring spectrum DB.

Keywords. Ring spectrum, formal group law, Andre-Quillen homology

AMS subject classification. Primary: 55U35. Secondary: 14L05.

DOI: 10.2140/gt.2004.8.335

E-print: arXiv:math.AT/0402372

Submitted to GT on 12 July 2003. (Revised 12 February 2004.) Paper accepted 30 January 2004. Paper published 14 February 2004.

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Stefan Schwede
Mathematisches Institut, Universitaet Bonn
53115 Bonn, Germany

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