Abstract

We prove that the natural map T(F) ∕ R → A₀(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.

Keywords

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

Mathematical Subject Classification

Primary: 19E15

Authors