## Stable Homotopy over the Steenrod Algebra (Memoirs of the American Mathematical Society)

### John H. Palmieri

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We apply the tools of stable homotopy theory to the study of modules over the mod $p$ Steenrod algebra $A^{*}$. More precisely, let $A$ be the dual of $A^{*}$; then we study the category $\mathsf{stable}(A)$ of unbounded cochain complexes of injective co modules over $A$, in which the morphisms are cochain homotopy classes of maps. This category is triangulated. Indeed, it is a stable homotopy category, so we can use Brown representability, Bousfield localization, Brown-Comenetz duality, and other homotopy-theoretic tools to study it. One focus of attention is the analogue of the stable homotopy groups of spheres, which in this setting is the cohomology of $A$, $\mathrm{Ext}_A^{**}(\mathbf{F}_p,\mathbf{F}_p)$. We also have nilpotence theorems, periodicity theorems, a convergent chromatic tower, and a number of other results.

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## 1.Stable Homotopy over the Steenrod Algebra (Memoirs of the American Mathematical Society)

ISBN 10: 0821826689 ISBN 13: 9780821826683
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Book Description Amer Mathematical Society, 2001. Condition: Very Good. Former Library book. Great condition for a used book! Minimal wear. Seller Inventory # GRP83371819