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

• Autores: Cristian D. González Avilés
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 1, 2008, págs. 51-56
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n1.a5
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• Resumen

  • 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