Reduction types of CM curves

Mentzelos Melistas

doi:10.48550/arXiv.2405.13414

Reduction types of CM curves

Mentzelos Melistas

Mathematics of Operations Research

Research output: Working paper › Preprint › Academic

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Abstract

We study the reduction properties of low genus curves whose Jacobian has complex multiplication. In the elliptic curve case, we classify the possible Kodaira types of reduction that can occur. Moreover, we investigate the possible Namikawa Ueno types that can occur for genus $2$ curves whose Jacobian has complex multiplication which is defined over the base field. We also produce bounds on the torsion subgroup of abelian varieties with complex multiplication defined over local fields.

Original language	English
Publisher	ArXiv.org
DOIs	https://doi.org/10.48550/arXiv.2405.13414
Publication status	Published - 22 May 2024

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math.NT

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10.48550/arXiv.2405.13414

2405.13414v1Final published version, 329 KB

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Reduction types of CM curves
Melistas, M., 6 Jul 2024, In: Pacific Journal of Mathematics. 329, 2, p. 233–257 25 p.
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Reduction types of CM curves

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Reduction types of CM curves

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