### Motivic symmetric spectra, by J.F. Jardine

This paper replaces
A^1-local symmetric
spectra (No. 302). The present version is quite different from the
original in terms of technical details, language, and length. Some
errors have also been corrected.

The paper demonstrates the existence of a theory of symmetric spectra
for the motivic stable category. The main results imply the
existence of a categorical model for the motivic stable
category which has an internal symmetric monoidal smash product.

More explicitly, it is shown that there is a proper closed simplicial
model category structure for the category of symmetric T-spectra,
suitably defined, on the smooth Nisnevich site of a noetherian scheme
of finite type. The weak equivalences for this structure are stable
equivalences, defined by analogy with the definitions given by Hovey,
Shipley and Smith for ordinary symmetric spectra and by Jardine for
presheaves of symmetric spectra, except that one suspends by the
Morel-Voevodsky object T, and the underlying unstable category is the
motivic closed model structure for simplicial presheaves on the
Nisnevich site. The homotopy category obtained from the category of
symmetric T-spectra is equivalent to the motivic stable category.

The details of the basic construction of the original proper closed
simplicial model structure underlying the motivic stable
category are required to handle the symmetric case, and are displayed
in the first three sections of this paper.

The paper can be found, for now, in a variety of file formats (dvi,
ps, pdf) at Jardine's web
site. It is to appear in Documenta Mathematica. In that event, the
files on Jardine's web page will be replaced by a link to the journal.

J.F. Jardine <jardine@uwo.ca>