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

Abstract

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 CHd (X)tors 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 CHd (X) is finitely generated for every d in the indicated range.