GLOBAL WEIERSTRASS EQUATIONS OF HYPERELLIPTIC CURVES
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | LIU, Qing | |
| dc.date | 2022 | |
| dc.date.accessioned | 2024-04-04T02:41:50Z | |
| dc.date.available | 2024-04-04T02:41:50Z | |
| dc.date.issued | 2022 | |
| dc.identifier.issn | 0002-9947 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191187 | |
| dc.description.abstractEn | Given a hyperelliptic curve C of genus g over a number field K and a Weierstrass model {\mathsrc C} of C over the ring of integers O_K (i.e. the hyperelliptic involution of C extends to {\mathsrc C} and the quotient is a smooth model of P1_K over OK), we give necessary and sometimes sufficient conditions for {\mathsrc C} to be defined by a global Weierstrass equation. In particular, if C has everywhere good reduction, we prove that it is defined by a global Weierstrass equation with invertible discriminant if the class number hK is prime to 2(2g+1), confirming a conjecture of M. Sadek. | |
| dc.language.iso | en | |
| dc.publisher | American Mathematical Society | |
| dc.title.en | GLOBAL WEIERSTRASS EQUATIONS OF HYPERELLIPTIC CURVES | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Mathématiques [math]/Géométrie algébrique [math.AG] | |
| bordeaux.journal | Transactions of the American Mathematical Society | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03617410 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03617410v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Transactions%20of%20the%20American%20Mathematical%20Society&rft.date=2022&rft.eissn=0002-9947&rft.issn=0002-9947&rft.au=LIU,%20Qing&rft.genre=article |
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