Skip to Main content Skip to Navigation
Theses

Théorie du potentiel sur les courbes en géométrie analytique non archimédienne. Applications à la théorie d'Arakelov

Abstract : Relying on V.G. Berkovich's viewpoint in analytic geometry over a non-Archimedean field k, we establish in this thesis that smooth k-analytic curves carry a natural potential theory, fully similar to the classical theory on Riemann surfaces (complex analytic curves). The initial motivation comes from R. Rumely's work on arithmetical implications of such a theory. Non-Archimedean potential theory has a strong geometric flavour, of which one makes use to define harmonic functions and to prove their basic properties. We then introduce a notion of smooth function, as well as a linear operator, analogue of the complex laplacian dd^c, which is studied through distribution theory. The last chapter deals with a generalization of one-dimensional Arakelov geometry relying on non-Archimedean potential theory. It is used to establish an equidistribution result for sequences of points of small height and to give a new proof for a theorem of Rumely on arithmetic capacities.
Document type :
Theses
Complete list of metadata

https://tel.archives-ouvertes.fr/tel-00010990
Contributor : Amaury Thuillier <>
Submitted on : Wednesday, November 16, 2005 - 9:44:26 AM
Last modification on : Thursday, January 7, 2021 - 4:22:11 PM
Long-term archiving on: : Friday, April 2, 2010 - 10:32:27 PM

Identifiers

  • HAL Id : tel-00010990, version 1

Citation

Amaury Thuillier. Théorie du potentiel sur les courbes en géométrie analytique non archimédienne. Applications à la théorie d'Arakelov. Mathématiques [math]. Université Rennes 1, 2005. Français. ⟨tel-00010990⟩

Share

Metrics

Record views

1606

Files downloads

1603