Vol. 1, No. 1, 2016

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On some negative motivic homology groups

Tohru Kohrita

Vol. 1 (2016), No. 1, 19–41
DOI: 10.2140/akt.2016.1.19

For an arbitrary separated scheme X of finite type over a finite field Fq and a negative integer j, we prove, under the assumption of resolution of singularities, that H1(X, (j)) is canonically isomorphic to H1(π0(X), (j)) if j = 1 or 2, and Hi(X, (j)) vanishes if i 2 and i j 1. As the group H1(π0(X), (j)) is explicitly known, this gives a explicit calculation of motivic homology of degree 1 and weight 1 or 2 of an arbitrary scheme over a finite field.

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motivic homology, schemes over finite fields
Mathematical Subject Classification 2010
Primary: 14F42
Secondary: 19E15
Received: 24 December 2014
Revised: 1 February 2015
Accepted: 15 February 2015
Published: 31 July 2015
Tohru Kohrita
Graduate School of Mathematics
Nagoya University
Nagoya, 464-8602