使用通用的艾博语拆分Brauer类

L’Enseignement Mathématique Pub Date : 2018-05-31 DOI:10.4171/lem/1009

Wei Ho, Max Lieblich

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引用次数: 3

摘要

我们证明了一个域上的每一个Brauer类在一个阿贝尔变项下都会在一个torsor上分裂。如果类的指标不等于2模4，我们证明了任何分裂类的正属光滑曲线的Albanese变种也分裂类，并且存在许多这样的分裂类曲线。我们证明，当指标与2模4相等时，这可能是假的，但是在Albanese中添加一个单一的1属因子足以分裂类。

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Splitting Brauer classes using the universal Albanese

We prove that every Brauer class over a field splits over a torsor under an abelian variety. If the index of the class is not congruent to 2 modulo 4, we show that the Albanese variety of any smooth curve of positive genus that splits the class also splits the class, and there exist many such curves splitting the class. We show that this can be false when the index is congruent to 2 modulo 4, but adding a single genus 1 factor to the Albanese suffices to split the class.

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L’Enseignement Mathématique

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