ON FREYD'S GENERATING HYPOTHESIS

Freyd's generating hypothesis in stable homotopy theory is revisitedand new consequences and equivalent forms of it are derived.A surprising such consequence is that I, the Brown–Comenetzdual of the sphere and the source of many counterexamples instable homotopy, is the cofibre of a self-map of a wedge ofspheres. It is also shown that a consequence of the generatinghypothesis, that the homotopy of a finite spectrum that is nota wedge of spheres can never be finitely generated as a moduleover _*S, is in fact true for many finite torsion spectra.     

Glycerin

Ohne Zusammenfassung     

Thermodynamics of aqueous EDTA systems: Apparent and partial molar heat capacities and volumes of aqueous strontium and barium EDTA

Apparent molar heat capacities and volumes have been determined for Na₂SrEDTA (aq) and Na₂BaEDTA (aq). Standard state partial molar heat capacities and volumes have been calculated as well as the partial molar properties at 0.1 m ionic strength that are needed for various thermodynamic calculations. Selected enthalpies and stability constants from the literature have been combined with out heat capacities to generate predicted stability constants to 200°C.     

Local Cohomology of BP*BP-Comodules

Given a spectrum X, we construct a spectral sequence of BP_*BP-comodulesthat converges to BP_*(L_nX), where L_nX is the Bousfield localizationof X with respect to the Johnson–Wilson theory E(n)_*.The E₂-term of this spectral sequence consists of the derivedfunctors of an algebraic version of L_n. We show how to calculatethese derived functors, which are closely related to local cohomologyof BP_*-modules with respect to the ideal I_n+1. 2000 MathematicsSubject Classification 55N22, 55P60, 16W30.     

Classifying subcategories of modules

Let be the quotient of a regular coherent commutative ring by a finitely generated ideal. In this paper, we classify all abelian subcategories of finitely presented -modules that are closed under extensions. We also classify abelian subcategories of arbitrary -modules that are closed under extensions and coproducts, when is commutative and Noetherian. The method relies on comparison with the derived category of .

     

Cotorsion pairs, model category structures, and representation theory

We make a general study of Quillen model structures on abelian categories. We show that they are closely related to cotorsion pairs, which were introduced by Salce [Sal79] and have been much studied recently by Enochs and coauthors [EJ00]. This gives a method of constructing model structures on abelian categories, which we illustrate by building two model structures on the category of modules over a (possibly noncommutative) Gorenstein ring. The homotopy category of these model structures is a generalization of the stable module category much used in modular representation theory. This stable module category has also been studied by Benson [Ben97]. Received: 14 December 2000; in final form: 17 December 2001 / Published online: 5 September 2002