Motivic complexes over finite fields and the ring of correspondences at the generic point

Abstract

Already in the 1960s Grothendieck understood that one could obtain an almost entirely satisfactory theory of motives over a finite field when one assumes the full Tate conjecture. In this note we prove a similar result for motivic complexes. In particular Beilinson's Q-algebra of "correspondences at the generic point" is then defined for all connected varieties. We compute this for all smooth projective varieties (hence also for varieties birational to such a variety).

References in corpus (2)

• Equivalence numérique et équivalence cohomologique pour les variétés abéliennes sur les corps finis
• The de Rham-Witt and Z_p-cohomologies of an algebraic variety

Cited by in corpus (1)

• The Tate conjecture over finite fields (AIM talk)