Local Projective Model Structures on Simplicial Presheaves

Blander, Benjamin A.

Department of Mathematics, University of Chicago, 5734, S University Ave., Chicago, IL 60637, U.S.A. e-mail: [email protected]

K-Theory 24(3):p 283-301, November 2001.

We introduce different model structures on the categories of simplicial presheaves and simplicial sheaves on some essentially small Gro-then-dieck site T and give some applications of these simplified model categories. In particular, we prove that the stable homotopy categories SH((Sm/k)Nis,A1) and SH((Sch/k)cdh,A1) are equivalent. This result was first proven by Voevodsky and our proof uses many of his techniques, but it does not use his theory of Δ-closed classes.