射影空间与格拉斯曼流形上的理想类映射
Ideal class maps on projective spaces and Grassmannians
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中文总结 AI 辅助
该研究针对数域上射影空间与格拉斯曼流形的理想类映射，证明其固定理想类纤维的弱逼近性质，引入射影空间态射的局部缺陷并刻画线性子空间像对应的理想类。
中文摘要 AI 辅助
我们研究数域上射影空间与格拉斯曼流形的理想类映射，证明了正维线性子空间及格拉斯曼流形上每个固定理想类纤维的弱逼近性质；还引入了射影空间态射的局部缺陷，用以将线性子空间像对应的理想类刻画为类群中有限个陪集的并集。
英文摘要
We study ideal class maps on projective spaces and Grassmannians over a number field. We prove weak approximation in every fixed ideal class fiber on positive-dimensional linear subspaces and on Grassmannians. We also introduce local defects of morphisms of projective spaces and use them to describe the ideal classes arising from the image of a linear subspace as a finite union of cosets in the class group.
