In the second half of the paper we restrict ourselves to Weil-etale cohomology of the motivic complex. We show that for smooth projective varieties over finite fields, finite generation of Weil-etale cohomology is equivalent to Weil-etale cohomology being an integral model of l-adic cohomology, and also equivalent to the conjunction of Tate's conjecture and (rational) equality of rational and numerical equivalence. We give several examples where these conjectures hold, and express special values of zeta functions in terms of Weil-etale cohomology.

The first version, posted May 14, 2002, has been updated March 26, 2003, by the author. The results are the same, but the exposition is slightly different.

A revised version has been posted April 23, 2004.

- 0565.bib (223 bytes)
- maref.dvi (127752 bytes) [April 23, 2004]
- maref.dvi.gz (48497 bytes)
- maref.pdf (326450 bytes)
- maref.ps.gz (124954 bytes)

Thomas H. Geisser <geisser@math.usc.edu>