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On unstable modules over the Dickson algebras, the Singer functors Rs and the functors Fixs

Abstract :

The category Ds–U of unstable modules over the Steenrod algebra equipped with a compatible module structure over the Dickson algebra Ds is studied at the prime 2, with applications to the Singer functor Rs, considered as a functor from unstable modules U to Ds–U. An explicit copresentation of RsM is given using Lannes’ T–functor when M is a reduced unstable module; applying Lannes’ functor Fixs, this is used to show that Rs gives a fully-faithful embedding of U in Ds–U. In addition, the right adjoint ℨs to Rs is introduced and is related to the indecomposables functor and the functor Fixs.

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https://hal.archives-ouvertes.fr/hal-01389189
Contributor : Okina Université d'Angers <>
Submitted on : Friday, October 28, 2016 - 10:22:54 AM
Last modification on : Monday, March 9, 2020 - 6:16:00 PM

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Geoffrey Powell. On unstable modules over the Dickson algebras, the Singer functors Rs and the functors Fixs. Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2012, 12 (4), pp.2451 - 2491. ⟨10.2140/agt.2012.12.2451⟩. ⟨hal-01389189⟩

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