Geometry & Topology
- Geom. Topol.
- Volume 8, Number 1 (2004), 335-412.
Formal groups and stable homotopy of commutative rings
We explain a new relationship between formal group laws and ring spectra in stable homotopy theory. We study a ring spectrum denoted which depends on a commutative ring and is closely related to the topological André–Quillen homology of . We present an explicit construction which to every 1–dimensional and commutative formal group law over associates a morphism of ring spectra 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 and . That description involves formal group law data and the homotopy units of the ring spectrum .
Geom. Topol., Volume 8, Number 1 (2004), 335-412.
Received: 12 July 2003
Revised: 12 February 2004
Accepted: 30 January 2004
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55U35: Abstract and axiomatic homotopy theory
Secondary: 14L05: Formal groups, $p$-divisible groups [See also 55N22]
Schwede, Stefan. Formal groups and stable homotopy of commutative rings. Geom. Topol. 8 (2004), no. 1, 335--412. doi:10.2140/gt.2004.8.335. https://projecteuclid.org/euclid.gt/1513883370