La formule de Noether pour les surfaces arithmétiques. (The Noether formula for arithmetic surfaces)

DOI10.1007/BF01393833zbMath0727.14014OpenAlexW2047194842MaRDI QIDQ803220

Laurent Moret-Bailly

Publication date: 1989

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143739

zbMATH Keywords

Mumford isomorphismarithmetic surfacesalgebraic stack of stable curvesArakelov's intersection pairingFaltings' Noether formula

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items (22)

Explicit Mumford isomorphism for hyperelliptic curves ⋮ Bounds on Faltings's delta function through covers ⋮ Local invariants attached to Weierstrass points ⋮ Effective bound of linear series on arithmetic surfaces ⋮ Determinant bundles, Quillen metrics and Mumford isomorphisms over the universal commensurability Teichmüller space ⋮ Bertini and Northcott ⋮ Unnamed Item ⋮ An arithmetic Hilbert-Samuel theorem for pointed stable curves ⋮ Hyperbolic superspaces and super-Riemann surfaces ⋮ Three-dimensional hyperbolic geometry as \(\infty\)-adic Arakelov geometry ⋮ Self-intersection of the relative dualizing sheaf on modular curves \(X_{ 1 }(N)\) ⋮ Symmetric roots and admissible pairing ⋮ Normal functions and the height of Gross-Schoen cycles ⋮ An Arakelov theoretic proof of the equality of conductor and discriminant ⋮ The arithmetic Riemann-Roch theorem and the Jacquet-Langlands correspondence ⋮ Semi-stable models of modular curves \(X_0(p^2)\) and some arithmetic applications ⋮ On CM points away from the Torelli locus ⋮ Weierstrass points on arithmetic surfaces ⋮ On the height of Gross-Schoen cycles in genus three ⋮ Décompositions en hauteurs locales ⋮ Hauteurs canoniques sur l'espace de modules des fibrés stables sur une courbe algébrique ⋮ Néron-Tate heights of cycles on jacobians

Cites Work

• Unnamed Item
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• Calculus on arithmetic surfaces
• The Mumford form and the Polyakov measure in string theory
• Conductor, discriminant, and the Noether formula of arithmetic surfaces
• Stability of projective varieties
• INTERSECTION THEORY OF DIVISORS ON AN ARITHMETIC SURFACE

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