Homogeneous vector bundles on abelian varieties which are (rigid) analytic tori
type: Item
instance of: scholarly article
title: Homogeneous vector bundles on abelian varieties which are (rigid) analytic tori
zbMATH Open document ID: 0611.14021
DOI: 10.1007/BF01168148
author: M. van der Put
author: Marc Reversat
published in: Manuscripta Mathematica
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155268
review text: This paper gives a characterization of homogeneous vector bundles on an abelian variety \(A\) (over a complete nonarchimedean valued field) which is an analytic torus, as the jacobians of the Mumford-curves for instance. Homogeneous vector bundles are stable under the action induced by the law of \(A\); it is proved that they are coming from the representations of the fundamental group of \(A\) fulfilling growth conditions, more precisely, that they are exactly those vector bundles which are constructed with the \(\Phi\)-bounded representations [this is a suitable adaptation of a notion introduced by \textit{G. Faltings}, Invent. Math. 74, 199--212 (1983; Zbl 0526.14018)].
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 14K15
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 14M25
zbMATH DE Number: 3987447
zbMATH Keywords: homogeneous vector bundles on an abelian variety
zbMATH Keywords: Jacobians of the Mumford-curves
zbMATH Keywords: \(\Phi\)-bounded representations
zbMATH Keywords: rigid analytic torus
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3987447