Abstract
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.
Citation
Agnès Beaudry. "The algebraic duality resolution at $p=2$." Algebr. Geom. Topol. 15 (6) 3653 - 3705, 2015. https://doi.org/10.2140/agt.2015.15.3653
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