Motivic complexes over finite fields and the ring of correspondences at the generic point
Algebraic Geometry
2021-01-19 v2 Number Theory
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).
Keywords
Cite
@article{arxiv.math/0607483,
title = {Motivic complexes over finite fields and the ring of correspondences at the generic point},
author = {James S. Milne and Niranjan Ramachandran},
journal= {arXiv preprint arXiv:math/0607483},
year = {2021}
}