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arXiv · 2609.23430

Mordell--Weil groups of quasi-elliptic surfaces in characteristic 3

Toshiyuki Katsura
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Abstract

In characteristic $p =3$, we establish a concrete relationship between the torsion rank of the elementary abelian group of global sections of quasi-elliptic surfaces over the projective line ${\mathbf P}^1$ and the $p$-rank of certain hyperelliptic curves, thereby explaining a mysterious relationship between these two invariants previously observed by I. Dolgachev. As an application, we determine the torsion ranks of the Mordell--Weil groups of a class of quasi-elliptic surfaces.

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BibTeXRIS

Toshiyuki Katsura. 2026-09-20. Mordell--Weil groups of quasi-elliptic surfaces in characteristic 3. https://arxiv.org/abs/2609.23430

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