A bound on the primes of bad reduction for CM curves of genus 3
| Autor: | Kristin E. Lauter, Rachel Newton, Marco Streng, Pınar Kılıçer, Ekin Ozman, Elisa Lorenzo García |
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| Přispěvatelé: | Carl Von Ossietzky Universität Oldenburg, Cryptography group, Microsoft Research [Redmond], Microsoft Corporation [Redmond, Wash.]-Microsoft Corporation [Redmond, Wash.], Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Department of Mathematics and Statistics, University of Reading, RG66AX, Reading UK, Bogazici University [Istanbul], Universiteit Leiden [Leiden], Microsoft Corporation [Redmond], Microsoft Corporation [Redmond, Wash.], Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), University of Reading (UOR), Boğaziçi University [Istanbul], 639.031.243, Engineering and Physical Sciences Research Council, Carl Von Ossietzky Universität Oldenburg = Carl von Ossietzky University of Oldenburg (OFFIS), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Boǧaziçi üniversitesi = Boğaziçi University [Istanbul], Universiteit Leiden, ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), Algebra |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Reduction (recursion theory)
General Mathematics Mathematics::Number Theory 010103 numerical & computational mathematics Algebraic geometry 01 natural sciences Prime (order theory) Combinatorics [ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT] Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Genus (mathematics) FOS: Mathematics Number Theory (math.NT) 0101 mathematics Abelian group Algebraic Geometry (math.AG) Mathematics Mathematics - Number Theory Applied Mathematics 010102 general mathematics 11G10 11G15 14H45 14K22 14J15 14Q05 [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] [ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG] Elliptic curve Finite field Number theory [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] |
| Zdroj: | 16 pages, some minor and major updates. 2016 Proceedings of the American Mathematical Society Proceedings of the American Mathematical Society, American Mathematical Society, 2020, 148 (7), pp.2843-2861. ⟨10.1090/proc/14975⟩ Proceedings of the American Mathematical Society, 2020, 148 (7), pp.2843-2861. ⟨10.1090/proc/14975⟩ Proceedings of the american mathematical society, 148(7), 2843-2861 Proceedings of the American Mathematical Society, 148(7), 2843-2861. American Mathematical Society (AMS) |
| ISSN: | 0002-9939 1088-6826 |
| DOI: | 10.1090/proc/14975 |
| Popis: | We give bounds on the primes of geometric bad reduction for curves of genus three of primitive CM type in terms of the CM orders. In the case of genus one, there are no primes of geometric bad reduction because CM elliptic curves are CM abelian varieties, which have potential good reduction everywhere. However, for genus at least two, the curve can have bad reduction at a prime although the Jacobian has good reduction. Goren and Lauter gave the first bound in the case of genus two. In the cases of hyperelliptic and Picard curves, our results imply bounds on primes appearing in the denominators of invariants and class polynomials, which are important for algorithmic construction of curves with given characteristic polynomials over finite fields. Comment: 16 pages, some minor updates, some typos are corrected |
| Databáze: | OpenAIRE |
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