Abstract
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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
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.
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Keywords
complex multiplication, elliptic curve, genus 2 curve,
Kodaira-type, reduction-type
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Mathematical Subject Classification
Primary: 11G05, 11G07, 14H25, 14K15, 14K22
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Milestones
Received: 1 January 2023
Revised: 19 January 2024
Accepted: 18 May 2024
Published: 6 July 2024
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| © 2024 MSP (Mathematical Sciences
Publishers). Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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