Algebraic & Geometric Topology

The algebraic duality resolution at $p=2$

Agnès Beaudry

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Abstract

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 2 whose kernel we denote by S21. The algebraic duality resolution is a finite resolution of the trivial 2[[S21]]–module 2 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 3[[G21]]–module 3 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.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 6 (2015), 3653-3705.

Dates
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
https://projecteuclid.org/euclid.agt/1510841080

Digital Object Identifier
doi:10.2140/agt.2015.15.3653

Mathematical Reviews number (MathSciNet)
MR3450774

Zentralblatt MATH identifier
1350.55019

Subjects
Primary: 55Q45: Stable homotopy of spheres
Secondary: 55T99: None of the above, but in this section 55P60: Localization and completion

Keywords
finite resolution K(2)-local chromatic homotopy theory

Citation

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


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