The algebraic duality resolution at p = 2

Beaudry, Agnès¹

¹Department of Mathematics, University of Chicago, 1118 East 58th Street, Chicago, IL 60637, USA

Algebraic and Geometric Topology, Tome 15 (2015) no. 6, pp. 3653-3705

Résumé

The goal of this paper is to develop some of the machinery necessary for doing K(2)–local computations in the stable homotopy category using duality resolutions at the prime p = 2. The Morava stabilizer group S2 admits a surjective homomorphism to ℤ2 whose kernel we denote by S21. The algebraic duality resolution is a finite resolution of the trivial ℤ2[[S21]]–module ℤ2 by modules induced from representations of finite subgroups of S21. Its construction is due to Goerss, Henn, Mahowald and Rezk. It is an analogue of their finite resolution of the trivial ℤ3[[G21]]–module ℤ3 at the prime p = 3. The construction was never published and it is the main result in this paper. In the process, we give a detailed description of the structure of Morava stabilizer group S2 at the prime 2. We also describe the maps in the algebraic duality resolution with the precision necessary for explicit computations.

Détail

DOI : 10.2140/agt.2015.15.3653

Classification : 55Q45, 55T99, 55P60
Keywords: finite resolution, K(2)-local, chromatic homotopy theory

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