Title of paper: Presheaves of chain complexes
Author: J.F. Jardine
AMS Classification numbers: 55P42 55U15 18G15
Address of Author: Department of Mathematics
University of Western Ontario
London, Ontario N6A 5B7
Canada
Email: jardine@uwo.ca
This paper gives the basic constructions for homology theory in the
category of modules over a presheaf of commutative rings with
unit. The category of simplicial modules inherits a proper closed
simplicial model structure from the category of simplicial
presheaves. The corresponding stable category is described by several
different models, including infinitely graded chain complexes,
spectrum objects in simplicial modules, and symmetric spectrum objects
in simplicial modules. The tensor product of simplicial modules
induces a symmetric monoidal tensor product on the category of
symmetric spectrum objects, by analogy with the construction of the
smash product for symmetric spectra.
This paper is in preliminary form only, and is expected to pass
through several revisions. Proofs of the displayed results are in
place, but it is expected that more material on Tor functors and the
relation with motivic homotopy theory will be added later.
The paper is available in dvi, ps and pdf formats at
Jardine's home page.