通过数域上的亏格1曲线分裂Brauer类
Splitting Brauer classes by genus one curves over number fields
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中文总结 AI 辅助
该研究证明数域上维数≥2的Severi-Brauer簇含扭曲椭圆正规曲线，进而得出数域上每个Brauer类都被亏格1曲线分裂的结论，所用方法为纤维化方法，核心是证明相关Hilbert概型光滑紧化的有理点在其Brauer-Manin集内稠密。
中文摘要 AI 辅助
我们证明，数域上每个维数至少为2的Severi-Brauer簇都包含一条扭曲椭圆正规曲线。因此，数域上的每个Brauer类都被一条亏格1曲线分裂。我们利用纤维化方法证明这一点，即证明扭曲椭圆正规曲线的Hilbert概型的光滑紧化上的有理点在其Brauer-Manin集合中是稠密的。
英文摘要
We prove that every Severi-Brauer variety of dimension at least two over a number field contains a twisted elliptic normal curve. Consequently, every Brauer class over a number field is split by a genus one curve. We prove this using the fibration method, by showing that the rational points on a smooth compactification of the Hilbert scheme of twisted elliptic normal curves are dense in its Brauer-Manin set.
