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

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

2006-07-20

arxiv.org/abs/math/0607483v2

Mathematics

Algebraic Geometry

Scientific paper

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).

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