Modèles entiers des courbes hyperelliptiques sur un corps de valuation discrète
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- by Qing Liu PDF
- Trans. Amer. Math. Soc. 348 (1996), 4577-4610 Request permission
Abstract:
Let $C$ be a hyperelliptic curve of genus $g\ge 1$ over a discrete valuation field $K$. In this article we study the models of $C$ over the ring of integers $\mathcal {O}_{K}$ of $K$. To each Weierstrass model (that is a projective model arising from a hyperelliptic equation of $C$ with integral coefficients), one can associate a (valuation of) discriminant. Then we give a criterion for a Weierstrass model to have minimal discriminant. We show also that in the most cases, the minimal regular model of $C$ over $\mathcal {O}_{K}$ dominates every minimal Weierstrass model. Some classical facts concerning Weierstrass models over $\mathcal {O}_{K}$ of elliptic curves are generalized to hyperelliptic curves, and some others are proved in this new setting.References
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Additional Information
- Qing Liu
- Affiliation: CNRS, Laboratoire de Mathématiques Pures, Université Bordeaux I, 351, Cours de la Libération, 33405 Talence Cedex, France
- MR Author ID: 240790
- Email: liu@math.u-bordeaux.fr
- Received by editor(s): August 22, 1995
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 348 (1996), 4577-4610
- MSC (1991): Primary 11G20, 14H25; Secondary 14G20
- DOI: https://doi.org/10.1090/S0002-9947-96-01684-4
- MathSciNet review: 1363944