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.
Notes on file formats
Stefan Schwede
Mathematisches Institut, Universitaet Bonn
53115 Bonn, Germany
Email: schwede@math.uni-bonn.de
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