Nous étudions l’exposant diophantien d’un point 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 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.
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Mots clés : espaces de réseaux, points rationnels, groupes orthogonaux, théorème du sous-espace
@article{AHL_2022__5__1009_0, author = {de Saxc\'e, Nicolas}, title = {Approximation diophantienne sur les quadriques}, journal = {Annales Henri Lebesgue}, pages = {1009--1034}, publisher = {\'ENS Rennes}, volume = {5}, year = {2022}, doi = {10.5802/ahl.142}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/ahl.142/} }
de Saxcé, Nicolas. Approximation diophantienne sur les quadriques. Annales Henri Lebesgue, Tome 5 (2022), pp. 1009-1034. doi : 10.5802/ahl.142. http://www.numdam.org/articles/10.5802/ahl.142/
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