Rendiconti del Seminario Matematico della Università di Padova

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Volume 119, 2008, pp. 21–95
DOI: 10.4171/RSMUP/119-2

Published online: 2008-06-30

Pentes des Fibrés Vectoriels Adéliques sur un Corps Global

Éric Gaudron[1]

(1) Université de Grenoble I, Saint-Martin-d'Hères, France

At the end of the twentieth century, J.-B. Bost developed a slope theory of hermitian vector bundles over number fields. A new method of diophantine approximation, the so-called slope method, has emerged from his research. Our article proposes a generalization to adelic vector bundles over global fields. The norms at the archimedean places are no longer supposed to be hermitian. The link with adelic successive minima is also mentioned. To get these results, we use several concepts from the geometry of finite dimensional Banach spaces.

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Gaudron Éric: Pentes des Fibrés Vectoriels Adéliques sur un Corps Global. Rend. Sem. Mat. Univ. Padova 119 (2008), 21-95. doi: 10.4171/RSMUP/119-2