准阿贝尔变体上的符号卷积

Pub Date : 2024-05-01 DOI:10.1016/j.indag.2024.04.006

Jakob Bergqvist, Thuong Dang, Stefan Schröer

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引用次数: 0

摘要

我们研究了无方变体扭曲形式上的所谓符号卷积，并证明了当且仅当魏尔-夏特莱群中的类被两个湮没时，才存在这样的符号卷积。如果这些等价条件成立，我们就能证明商的皮卡方案是 étale 的，并且不包含有限阶点。在维数一中，这种商是布劳尔-塞维里曲线，我们分析了随之而来的属一曲线嵌入希尔泽布鲁赫曲面和加权投影空间的扭曲形式。

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Sign involutions on para-abelian varieties

We study the so-called sign involutions on twisted forms of abelian varieties, and show that such a sign involution exists if and only if the class in the Weil–Châtelet group is annihilated by two. If these equivalent conditions hold, we prove that the Picard scheme of the quotient is étale and contains no points of finite order. In dimension one, such quotients are Brauer–Severi curves, and we analyze the ensuing embeddings of the genus-one curve into twisted forms of Hirzebruch surfaces and weighted projective spaces.

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