- For X as above, the algebraicity of the Kunneth components of the diagonal and the hard Lefschetz theorem for cycles modulo numerical equivalence.

- The existence of Beilinson's conjectural filtration on Chow groups: for X as above and n>0, there is a separated filtration of length n+1 on the n-th Chow group of X, stable under the action of correspondences and such that, on the associated graded, this action factors through numerical equivalence.

- The rational Bass conjecture: for any smooth variety X over F_p, the algebraic K-groups of X are, after tensoring with Q, finite dimensional vector spaces.

- The Bass-Tate conjecture: for F a field of characteristic p, of absolute transcendence degree d, the i-th Milnor K-group of F is torsion for i>d.

- Soulé's conjecture: given a quasi-projective variety X over F_p, the order of the zero of its Hasse-Weil zeta function at an integer n is given by the alternating sum of the ranks of the weight n part of its algebraic K'-groups.

- 0247.bib (239 bytes)
- Tate.dvi (301780 bytes) [January 6, 1998]
- Tate.dvi.gz (105784 bytes)
- Tate.pdf (428128 bytes)
- Tate.ps.gz (347008 bytes)

Bruno Kahn <kahn@math.jussieu.fr>