Approximation diophantienne sur les quadriques

de Saxcé, Nicolas

Annales Henri Lebesgue, Tome 5 (2022), pp. 1009-1034

Nous étudions l’exposant diophantien d’un point $x$ d’une hypersurface quadratique. Nous montrons notamment un analogue du théorème de Thue–Siegel–Roth, c’est-à-dire une formule pour l’exposant diophantien d’un point algébrique, et un analogue du résultat de Kleinbock et Margulis sur l’extrémalité des sous-variétés non dégénérées de l’espace affine.

We study the Diophantine exponent of a point $x$ on a quadric hypersurface. We show in particular an analogue of the Thue–Siegel–Roth theorem, that is to say a formula for the Diophantine exponent of an algebraic point, and an analogue of the result of Kleinbock and Margulis on the extremality of non-degenerate analytic manifolds in the of affine space.

Classification : 11J83, 11J87, 37A17
Mots-clés : espaces de réseaux, points rationnels, groupes orthogonaux, théorème du sous-espace

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