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Quillen stratification for the Steenrod algebra

John H. Palmieri
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Abstract

Let A be the mod 2 Steenrod algebra, and let Q denote the category of exterior sub-Hopf algebras of A, where the morphisms are given by inclusions. The restriction maps Ext_A (Z/2,Z/2) --> Ext_E (Z/2,Z/2), for E in Q, can be assembled into a map i:Ext_A (Z/2, Z/2) --> lim_Q Ext_E (Z/2,Z/2). There is an action of A on this inverse limit, and i factors through the invariants under this action, giving a map g:Ext_A (Z/2, Z/2) --> ( lim_Q Ext_E (Z/2,Z/2) )^A. We show that g is an F-isomorphism.

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John H. Palmieri. 1999-03-01. Quillen stratification for the Steenrod algebra. https://arxiv.org/abs/math/9903202

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