On the Hasse principle for zero-cycles on Severi-Brauer fibrations

2005/05/13 by Gonzalez-Aviles, Cristian D.
#14C15 #14C25 #14K15 #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0505294

Abstract

The Abstract for this revised version is the following: Let k be a number field, let C be a smooth, projective and geometrically integral k-curve and let p:X --> C be a Severi-Brauer k-fibration of squarefree index. Various authors have studied the cokernel of the natural map CH₀(X/C)-->\bigoplus_vCH₀(X_v/C_v), where CH₀(X/C) is the kernel of p_*:CH₀(X)-->CH₀(C). In this paper I obtain an exact sequence which relates the Tate-Shafarevich group of the kernel of the above map to the Tate-Shafarevich group of the Neron-Severi torus of X. I then obtain conditions under which these two groups agree.

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