Stable homotopy over the Steenrod algebra
Author(s)
Bibliographic Information
Stable homotopy over the Steenrod algebra
（Memoirs of the American Mathematical Society, no. 716）
American Mathematical Society, 2001
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"May 2001, volume 151, number 716 (second of 5 numbers)"
Includes bibliographical references (p. 165-168) and index
Description and Table of Contents
Description
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.
Table of Contents
Preliminaries Stable homotopy over a Hopf algebra Basic properties of the Steenrod algebra Chromatic structure Computing Ext with elements inverted Quillen stratification and nilpotence Periodicity and other applications of the nilpotence theorems Appendix A. An underlying model category Appendix B. Steenrod operations and nilpotence in $\mathrm{Ext}_\Gamma^{**}(k,k)$ Bibliography Index.
by "Nielsen BookData"
