Arithmetic Hilbert-Samuel theorem

DOI10.5802/aif.1458zbMath0818.14011OpenAlexW2032024317MaRDI QIDQ1891884

Thierry Bouche, Ahmed Abbes

Publication date: 1 June 1995

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1995__45_2_375_0

zbMATH Keywords

arithmetic varietyarithmetic intersectionArakelov theoremarithmetic Hilbert-Samuel theoremsections of an ample line bundle

Mathematics Subject Classification ID

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Arithmetic algebraic geometry (Diophantine geometry) (11G99) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items

On the Bertini regularity theorem for arithmetic varieties, Small points and the Bogomolov conjecture, Mahler measures and logarithmic equidistribution, An arithmetic Hilbert–Samuel theorem for singular hermitian line bundles and cusp forms, Capacity theory and arithmetic intersection theory, Metrised ample line bundles in non-Archimedean geometry, On the global determinant method, Equidistribution of subvarieties of small height, Big arithmetic divisors on the projective spaces over \(\mathbb{Z}\), On isoperimetric inequality in Arakelov geometry, Numerical characterization of nef arithmetic divisors on arithmetic surfaces, An Adams-Riemann-Roch theorem in Arakelov geometry, Big line bundles over arithmetic varieties, Boundedness of the successive minima on arithmetic varieties, Distribution of logarithmic spectra of the equilibrium energy, Introduction to arithmetic Hilbert-Samuel theorems, Arakelov geometry, heights, equidistribution, and the Bogomolov conjecture, Okounkov bodies of filtered linear series, Valuations, intersections and Belyi functions--some remarks on the construction of heights, Explicit majorizations of geometric and arithmetic Hilbert-Samuel functions, On the slopes of the lattice of sections of hermitian line bundles, Continuity of volumes on arithmetic varieties, The theta invariants and the volume function on arithmetic varieties

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