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arXiv · 2006.07987

High $\ell$-torsion rank for class groups over function fields

Iman Setayesh·Jacob Tsimerman
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Abstract

We prove that in the function field setting, $\ell$-torsion in the class groups of quadratic fields can be arbitrarily large. In fact, we explicitly produce a family whose $\ell$-rank growth matches the growth in the setting of genus theory, which might be best possible. We do this by specifically focusing on the Artin-Schreir curves $y^2=x^q-x$.

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Iman Setayesh, Jacob Tsimerman. 2020-06-14. High $\ell$-torsion rank for class groups over function fields. https://arxiv.org/abs/2006.07987

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