Homogeneous vector bundles on abelian varieties which are (rigid) analytic tori
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)].
homogeneous vector bundles on an abelian variety
scientific article; zbMATH DE number 3987447
scientific article