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2016 On some negative motivic homology groups
Tohru Kohrita
Ann. K-Theory 1(1): 19-41 (2016). DOI: 10.2140/akt.2016.1.19

Abstract

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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Tohru Kohrita. "On some negative motivic homology groups." Ann. K-Theory 1 (1) 19 - 41, 2016. https://doi.org/10.2140/akt.2016.1.19

Information

Received: 24 December 2014; Revised: 1 February 2015; Accepted: 15 February 2015; Published: 2016
First available in Project Euclid: 12 December 2017

zbMATH: 1329.14046
MathSciNet: MR3514935
Digital Object Identifier: 10.2140/akt.2016.1.19

Subjects:
Primary: 14F42
Secondary: 19E15

Keywords: motivic homology , schemes over finite fields

Rights: Copyright © 2016 Mathematical Sciences Publishers

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