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Unstable modules over the Steenrod algebra revisited

Geoffrey M L Powell

Geometry & Topology Monographs 11 (2007) 245–288

DOI: 10.2140/gtm.2007.11.245

arXiv: 0903.4992

Abstract

A new and natural description of the category of unstable modules over the Steenrod algebra as a category of comodules over a bialgebra is given; the theory extends and unifies the work of Carlsson, Kuhn, Lannes, Miller, Schwartz, Zarati and others. Related categories of comodules are studied, which shed light upon the structure of the category of unstable modules at odd primes. In particular, a category of bigraded unstable modules is introduced; this is related to the study of modules over the motivic Steenrod algebra.

Keywords

Steenrod algebra, unstable module, tensor abelian category, functor category

Mathematical Subject Classification

Primary: 55S10

Secondary: 18E10

References
Publication

Received: 10 February 2005
Revised: 1 July 2005
Accepted: 24 October 2005
Published: 14 November 2007

Authors
Geoffrey M L Powell
Laboratoire Analyse Géométrie et Applications
UMR 7539
Institut Galilée
Université Paris 13
93430 Villetaneuse
France
http://www.math.univ-paris13.fr/~powell/