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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Article dans une revue
Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2012, 12 (4), pp.2451 - 2491. 〈http://www.msp.warwick.ac.uk/agt/2012/12-04/agt-2012-12-091s.pdf〉. 〈10.2140/agt.2012.12.2451〉
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https://hal.archives-ouvertes.fr/hal-01389189
Contributeur : Okina Université d'Angers <>
Soumis le : vendredi 28 octobre 2016 - 10:22:54
Dernière modification le : lundi 5 février 2018 - 15:00:03

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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. 〈http://www.msp.warwick.ac.uk/agt/2012/12-04/agt-2012-12-091s.pdf〉. 〈10.2140/agt.2012.12.2451〉. 〈hal-01389189〉

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