By John H. Palmieri

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

**Read Online or Download Stable Homotopy over the Steenrod Algebra (Memoirs of the American Mathematical Society) PDF**

**Similar Algebraic Geometry books**

**Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics)**

This new-in-paperback version offers a basic advent to algebraic and mathematics geometry, beginning with the idea of schemes, via functions to mathematics surfaces and to the speculation of aid of algebraic curves. the 1st half introduces uncomplicated gadgets corresponding to schemes, morphisms, base swap, neighborhood homes (normality, regularity, Zariski's major Theorem).

**Essays in Constructive Mathematics**

Contents and remedy are clean and extremely diverse from the traditional remedies offers an absolutely optimistic model of what it capability to do algebra The exposition isn't just transparent, it truly is pleasant, philosophical, and thoughtful even to the main naive or green reader

First textbook-level account of simple examples and strategies during this region. appropriate for self-study through a reader who understands a bit commutative algebra and algebraic geometry already. David Eisenbud is a well known mathematician and present president of the yankee Mathematical Society, in addition to a profitable Springer writer.

**Ramanujan's Lost Notebook: Part I (Pt. 1)**

Within the library at Trinity collage, Cambridge in 1976, George Andrews of Pennsylvania nation collage chanced on a sheaf of pages within the handwriting of Srinivasa Ramanujan. quickly precise as "Ramanujan’s misplaced Notebook," it comprises enormous fabric on mock theta capabilities and unquestionably dates from the final 12 months of Ramanujan’s existence.

**Extra resources for Stable Homotopy over the Steenrod Algebra (Memoirs of the American Mathematical Society)**