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Algebraic Geometry

# Download E-books Stable Homotopy over the Steenrod Algebra (Memoirs of the American Mathematical Society) PDF

By John H. Palmieri

We observe the instruments of solid homotopy idea to the examine of modules over the mod $p$ Steenrod algebra $A^{*}$. extra accurately, permit $A$ be the twin of $A^{*}$; then we learn the class $\mathsf{stable}(A)$ of unbounded cochain complexes of injective co modules over $A$, during which the morphisms are cochain homotopy sessions of maps. This type is triangulated. certainly, it's a solid homotopy class, for you to use Brown representability, Bousfield localization, Brown-Comenetz duality, and different homotopy-theoretic instruments to review it. One concentration of awareness is the analogue of the good homotopy teams of spheres, which during this surroundings is the cohomology of $A$, $\mathrm{Ext}_A^{**}(\mathbf{F}_p,\mathbf{F}_p)$. We even have nilpotence theorems, periodicity theorems, a convergent chromatic tower, and several effects.

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