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Theses

Espaces de Berkovich sur Z

Abstract : At the end of the eighties, Vladimir G. Berkovich defined a notion of analytic space over any Banach ring. Our thesis is devoted to the special case where this Banach ring is Z or the ring of integers of a number field.

Most of our work deals with the analytic line. We manage to show it shares many properties with the usual complex analytic spaces : the topological space is locally arcwise connected, the local rings are Henselian and Noetherian, the structure sheaf is coherent, the disks have no coherent cohomology, etc.

At last, we explain how these general results can be used to derive some properties of convergent arithmetic power series, for example holomorphic functions over C whose developpement in one prescribed point has integer coefficients.
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https://tel.archives-ouvertes.fr/tel-00193626
Contributor : Jérôme Poineau <>
Submitted on : Tuesday, December 4, 2007 - 11:12:57 AM
Last modification on : Thursday, January 7, 2021 - 4:25:27 PM
Long-term archiving on: : Monday, April 12, 2010 - 5:58:44 AM

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  • HAL Id : tel-00193626, version 1

Citation

Jérôme Poineau. Espaces de Berkovich sur Z. Mathématiques [math]. Université Rennes 1, 2007. Français. ⟨tel-00193626⟩

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