Ideal class maps on projective spaces and Grassmannians

Yufan Liu

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arXiv · 2608.14623

Ideal class maps on projective spaces and Grassmannians

Yufan Liu

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Abstract

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.

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Yufan Liu. 2026-07-16. Ideal class maps on projective spaces and Grassmannians. https://arxiv.org/abs/2608.14623

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