A nilpotence theorem for modules over the mod 2 Steenrod algebra
type: Item
instance of: scholarly article
title: A nilpotence theorem for modules over the mod 2 Steenrod algebra
zbMATH Open document ID: 0801.55011
DOI: 10.1016/0040-9383(93)90049-2
published in: Topology
publication date: 1994-04-12T00:00:00Z
review text: The authors give a characterization of the nilpotent elements of \(\text{Ext}_ A^{**}({\mathbf F}_ 2,{\mathbf F}_ 2)\), where \(A\) denotes a sub-Hopf algebra of the mod 2 Steenrod algebra, thereby proving a conjecture of Adams. Call a sub-Hopf algebra of \(A\) elementary if it is an exterior algebra. The main result of the paper is that an element of \(\text{Ext}_ A^{**}({\mathbf F}_ 2,{\mathbf F}_ 2)\) is nilpotent if its restrictions to all elementary sub-Hopf algebras of \(A\) vanish. This result is part of a program for proving structure theorems for Steenrod algebra modules analogous to the results of Devinatz, Hopkins and Smith for spectra.
Mathematics Subject Classification ID: 55S10
zbMATH DE Number: 550342
zbMATH Keywords: nilpotence theorem
zbMATH Keywords: mod 2 Steenrod algebra
author: Michael J. Hopkins
author: John H. Palmieri
reviewed by: Peter Landweber
MaRDI profile type: Publication
full work available at URL: 0040-9383(93)90049-2
OpenAlex ID: W2029249059
Wikidata QID: Q127065713
description: scientific article; zbMATH DE number 550342