Stable homotopy over the Steenrod algebra

Autor: Palmieri, John H.
Rok: 2001.
ISBN: 9780821826683
OKCZID: 110358179

Citace (dle ČSN ISO 690):
PALMIERI, John H. Stable homotopy over the Steenrod algebra. Providence: American Mathematical Society, 2001. xix, 172 s. Memoirs of the American Mathematical Society, nr. 716.

Anotace

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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