Elliptic surfaces to class groups and Selmer groups

Kalyan Banerjee; Kalyan Chakraborty; Azizul Hoque

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arXiv · 2509.00551

Elliptic surfaces to class groups and Selmer groups

Kalyan Banerjee·Kalyan Chakraborty·Azizul Hoque

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Abstract

In this note, we connect the $n$-torsions of the Picard group of an elliptic surface to the $n$-divisibility of the class group of torsion fields for a given integer $n>1$. We also connect the $n$-divisibility of the Selmer group to that of the class group of torsion fields.

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BibTeX RIS

Kalyan Banerjee, Kalyan Chakraborty, Azizul Hoque. 2025-08-30. Elliptic surfaces to class groups and Selmer groups. https://arxiv.org/abs/2509.00551

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