Groupe de Chow de codimension deux des vari�t�s d�finies sur un corps de nombres: un th�or�me de finitude pour la torsion

Colliot-Thélène, Jean-Louis; Raskind, Wayne

doi:10.1007/bf01232266

Cited by 34 publications

(20 citation statements)

References 28 publications

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“…Thus if d is even, CH 0 (X ) has an infinite torsion subgroup after a suitable unramified base change. Theorem 1.1 may be compared with the finiteness results [Colliot-Thélène and Raskind 1991] and [Raskind 1989] on CH 0 (X ) tor for a surface X over a p-adic field under the assumption that H 2 (X, ᏻ X ) = 0 or, more generally, that the rank of the Néron-Severi group does not change by reduction. For a nonsingular surface X ⊂ ‫ސ‬ …”

Section: Introductionmentioning

confidence: 99%

Surfaces over a p-adic field with infinite torsion in the Chow group of 0-cycles

Asakura

Saito

2007

ANT

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Section: Introductionmentioning

confidence: 99%

Surfaces over a p-adic field with infinite torsion in the Chow group of 0-cycles

Asakura

Saito

2007

ANT

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“…D. Harari proves a similar result about Brauer groups, see [19]. Arguments similar to the ones used in this section can also be found in [7,18]. Proposition 6.2 will be used in the next section to find the Néron-Severi group of the elliptic surface Y Q from the previous section and the Mordell-Weil group E(Q(s)) of its generic fiber E.…”

Section: The Néron-severi Group Under Good Reductionmentioning

confidence: 65%

An elliptic K3 surface associated to Heron triangles

Luijk

2007

Journal of Number Theory

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A rational triangle is a triangle with rational sides and rational area. A Heron triangle is a triangle with integral sides and integral area. In this article we will show that there exist infinitely many rational parametrizations, in terms of s, of rational triangles with perimeter 2s(s + 1) and area s(s 2 − 1). As a corollary, there exist arbitrarily many Heron triangles with all the same area and the same perimeter. The proof uses an elliptic K3 surface Y . Its Picard number is computed to be 18 after we prove that the Néron-Severi group of Y injects naturally into the Néron-Severi group of the reduction of Y at a prime of good reduction. We also give some constructions of elliptic surfaces and prove that under mild conditions a cubic surface in P 3 can be given the structure of an elliptic surface by cutting it with the family of hyperplanes through a given line L. Some of these constructions were already known, but appear to have lacked proof in the literature until now.

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“…Previous work on Bloch's conjecture include [3], where CH 2 (X) is shown to be finitely generated for a certain class of varieties X, and [4], where the same result is obtained for CH 0 (X) when X → C is an arbitrary (i.e., not necessarily smooth over C) Severi-Brauer fibration of squarefree index.…”

Section: Introductionmentioning

confidence: 66%

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

González-Avilés

2008

Mathematical Research Letters

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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)tors contains a subgroup isomorphic to CH 0 (X/C) for every d in the range 2 ≤ d ≤ p. We deduce that, if k is a number field, the full Chow ring CH * (X) is a finitely generated abelian group.

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Groupe de Chow de codimension deux des vari�t�s d�finies sur un corps de nombres: un th�or�me de finitude pour la torsion

Cited by 34 publications

References 28 publications

Surfaces over a p-adic field with infinite torsion in the Chow group of 0-cycles

Surfaces over a p-adic field with infinite torsion in the Chow group of 0-cycles

An elliptic K3 surface associated to Heron triangles

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

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