Applications of the fibration method for zero-cycles to the Brauer-Manin obstruction to the existence of zero-cycles on certain varieties

Evis Ieronymou

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arXiv · 2201.01178

Applications of the fibration method for zero-cycles to the Brauer-Manin obstruction to the existence of zero-cycles on certain varieties

Evis Ieronymou

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Abstract

We study the Brauer-Manin obstruction to the existence of zero-cycles of degree $d$ on certain classes of varieties over number fields. We generalise existing results in the literature and prove some results about fibrations over the projective line, where the geometric Brauer group of the generic fibre is not assumed to be finite. The idea is to assume that the Brauer-Manin obstruction to the Hasse principle is the only one for certain fibres and then deduce analogous results for zero-cycles.

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BibTeX RIS

Evis Ieronymou. 2022-06-10. Applications of the fibration method for zero-cycles to the Brauer-Manin obstruction to the existence of zero-cycles on certain varieties. https://arxiv.org/abs/2201.01178

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