\(S\)-modules in the category of schemes. (English) Zbl 1024.55006

Hu, Po

Mem. Am. Math. Soc. 767, 125 p. (2003).

The monograph is a contribution to stable homotopy theory of algebraic varieties over a field \(k\). In [V. Voevodsky, The Milnor conjecture, preprint, 1996], Voevodsky introduced a triangulated stable homotopy category of spectra over \(k\). The purpose of the monograph is to construct an underlying rigid category of spectra over \(k\). The construction is based on the notion of coordinate-free algebraic spectra. In topology, such spectra are indexed on finite-dimensional subspaces of an infinite-dimensional linear product space over \(\mathbb{R}\). In the algebraic case, spectra will be indexed on subspaces of finite codimension of an infinite-dimensional free module over a Noetherian domain. In the homotopical part of the monograph closed model structures on the categories of algebraic spectra are given.

Reviewer: K.H.Kamps (Hagen)

MSC:

55P42	Stable homotopy theory, spectra
14F42	Motivic cohomology; motivic homotopy theory
55P48	Loop space machines and operads in algebraic topology
55P43	Spectra with additional structure (\(E_\infty\), \(A_\infty\), ring spectra, etc.)
55U35	Abstract and axiomatic homotopy theory in algebraic topology
55-02	Research exposition (monographs, survey articles) pertaining to algebraic topology

Keywords:

\(E_\infty\)-ring spectra; \(S\)-modules; motivic cohomology; stable homotopy theory; spectra; closed model structures