Pentes des fibrés vectoriels adéliques sur un corps global

Éric Gaudron (1)

1 IF - Institut Fourier

At the end of the twentieth century, J.-B. Bost developped 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 generalisation 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.

Mots clés: adelic vector bundle; adelic degree; John vector bundle; volume ratio; Banach-Mazur distance; adelic slope inequalities; adelic successive minima; maximal slope

Domaines: Théorie des nombres [math.NT]

Éric Gaudron. Pentes des fibrés vectoriels adéliques sur un corps global. Rendiconti del Seminario Matematico della Università di Padova, 2008, 119, pp.21-95. ⟨hal-00068904v2⟩