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

2007/01/29 by Cristian D. González-Avilés, Gonzalez-Aviles, Cristian D.
Arts and Humanities · Mathematics · #14C15 #14C25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0701861

openalex publication_date 2007/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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)_\rmtors contains a subgroup isomorphic to CH₀(X/C) for every d in the range 2≤ d≤ 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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