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2008 R-equivalence on three-dimensional tori and zero-cycles
Alexander Merkurjev
Algebra Number Theory 2(1): 69-89 (2008). DOI: 10.2140/ant.2008.2.69


We prove that the natural map T(F)RA0(X), where T is an algebraic torus over a field F of dimension at most 3, X a smooth proper geometrically irreducible variety over F containing T as an open subset and A0(X) is the group of classes of zero-dimensional cycles on X of degree zero, is an isomorphism. In particular, the group A0(X) is finite if F is finitely generated over the prime subfield, over the complex field, or over a p-adic field.


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Alexander Merkurjev. "R-equivalence on three-dimensional tori and zero-cycles." Algebra Number Theory 2 (1) 69 - 89, 2008.


Received: 28 June 2007; Revised: 23 October 2007; Accepted: 20 November 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1210.19005
MathSciNet: MR2377363
Digital Object Identifier: 10.2140/ant.2008.2.69

Primary: 19E15

Keywords: $K\!$-cohomology , $R$-equivalence , algebraic tori , zero-dimensional cycle

Rights: Copyright © 2008 Mathematical Sciences Publishers

Vol.2 • No. 1 • 2008
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