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

James S. Milne·Niranjan Ramachandran
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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).

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James S. Milne, Niranjan Ramachandran. 2008-05-03. Motivic complexes over finite fields and the ring of correspondences at the generic point. https://arxiv.org/abs/math/0607483

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