Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 15, Number 6 (2015), 3653-3705.
The algebraic duality resolution at $p=2$
The goal of this paper is to develop some of the machinery necessary for doing –local computations in the stable homotopy category using duality resolutions at the prime . The Morava stabilizer group admits a surjective homomorphism to whose kernel we denote by . The algebraic duality resolution is a finite resolution of the trivial –module by modules induced from representations of finite subgroups of . Its construction is due to Goerss, Henn, Mahowald and Rezk. It is an analogue of their finite resolution of the trivial –module at the prime . 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 at the prime . We also describe the maps in the algebraic duality resolution with the precision necessary for explicit computations.
Algebr. Geom. Topol., Volume 15, Number 6 (2015), 3653-3705.
Received: 19 December 2014
Revised: 30 March 2015
Accepted: 14 April 2015
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Beaudry, Agnès. The algebraic duality resolution at $p=2$. Algebr. Geom. Topol. 15 (2015), no. 6, 3653--3705. doi:10.2140/agt.2015.15.3653. https://projecteuclid.org/euclid.agt/1510841080