Conductor, discriminant, and the Noether formula of arithmetic surfaces

DOI10.1215/S0012-7094-88-05706-7zbMath0657.14017MaRDI QIDQ1110600

Takeshi Saito

Publication date: 1988

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

conductordiscriminantdifferentials of proper smooth curves

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Families, moduli of curves (algebraic) (14H10) Relevant commutative algebra (14A05)

Related Items (23)

Néron models, Lie algebras, and reduction of curves of genus one ⋮ Local invariants attached to Weierstrass points ⋮ Bad reduction of genus curves with CM jacobian varieties ⋮ Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture ⋮ Arithmetic of hyperelliptic curves over local fields ⋮ COMPUTINGL-FUNCTIONS AND SEMISTABLE REDUCTION OF SUPERELLIPTIC CURVES ⋮ Elliptic fibers over non-perfect residue fields. ⋮ Riemann-Roch isometries in the non-compact orbifold setting ⋮ 3-torsion and conductor of genus 2 curves ⋮ Most odd degree hyperelliptic curves have only one rational point ⋮ Direct images in non-archimedean Arakelov theory ⋮ Modèles entiers des courbes hyperelliptiques sur un corps de valuation discrète ⋮ An Arakelov theoretic proof of the equality of conductor and discriminant ⋮ On the conductor formula of Bloch ⋮ Enriques surfaces with normal \(K3\)-like coverings ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Zeta integrals on arithmetic surfaces ⋮ On the Brauer-Siegel ratio for abelian varieties over function fields ⋮ Unnamed Item ⋮ An isomorphism of the Deligne-Riemann-Roch type ⋮ An effective proof of the hyperelliptic Shafarevich conjecture ⋮ La formule de Noether pour les surfaces arithmétiques. (The Noether formula for arithmetic surfaces)

Cites Work

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• Resolution of surface singularities. Three lectures with an appendix by H. Hironaka. Ed. by U. Orbanz
• Calculus on arithmetic surfaces
• The Mumford form and the Polyakov measure in string theory
• Stability of projective varieties
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• Vanishing Cycles and Geometry of Curves Over a Discrete Valuation Ring
• The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
• Elliptic Curves and Wild Ramification
• Curves Over Discrete Valuation Rings

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