Mathematical Research Letters

Volume 15 (2008)

Number 1

Algebraic cycles on Severi-Brauer schemes of prime degree over a curve

Pages: 51 – 56



Cristian D. González-Avilés (Universidad Andrés Bello)


Let $k$ be a perfect field and let $p$ be a prime number different from the characteristic of $k$. Let $C$ be a smooth, projective and geometrically integral $k$-curve and let $X$ be a Severi-Brauer $C$-scheme of relative dimension $p-1$ . In this paper we show that $CH^{d}(X)_{{\rm{tors}}}$ contains a subgroup isomorphic to $CH_{0}(X/C)$ for every $d$ in the range $2\leq d\leq p$. We deduce that, if $k$ is a number field, the full Chow ring $CH^{*}\be(X)$ is a finitely generated abelian group.

Published 1 January 2008