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

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

2007-01-29

arxiv.org/abs/math/0701861v1

Mathematics

Number Theory

6 pages

Scientific paper

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, then $CH^{d}(X)$ is finitely generated for every $d$ in the indicated range.

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