An analytic viewpoint on the Hasse principle
[Un point de vue analytique sur le principe de Hasse]
Mehmeti, Vlerë1
1Sorbonne Université and Paris Cité, CNRS, IMJ-PRG, F-75005 Paris, France
Journal de l’École polytechnique — Mathématiques, Tome 11 (2024), pp. 875-908

Working on non-Archimedean analytic curves, we propose a geometric approach to the study of the Hasse principle over function fields of curves defined over a complete discretely valued field. Using it, we show the Hasse principle to be verified for certain families of projective homogeneous spaces. As a consequence, we prove that said principle holds for quadratic forms and homogeneous varieties over unitary groups, results originally shown in [8], [36], and [33].

En travaillant sur des courbes analytiques non archimédiennes, nous proposons une approche géométrique de l’étude du principe de Hasse sur les corps de fonctions des courbes définies sur un corps discrètement valué complet. En l’utilisant, nous montrons que le principe de Hasse est vérifié pour certaines familles d’espaces projectifs homogènes. En conséquence, nous prouvons que ce principe est valable pour les formes quadratiques et les variétés homogènes sur les groupes unitaires, résultats initialement démontrés dans [8], [36], et [33].

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jep.268
Classification : 14G22, 11E08, 12J25
Keywords: Local-global principle, Hasse principle, Berkovich curve, discrete valuation, homogeneous space, quadratic form
Mots-clés : Principe local-global, principe de Hasse, courbe de Berkovich, valuation discrète, espace homogène, forme quadratique

Mehmeti, Vlerë  1

1 Sorbonne Université and Paris Cité, CNRS, IMJ-PRG, F-75005 Paris, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Mehmeti, Vlerë. An analytic viewpoint on the Hasse principle. Journal de l’École polytechnique — Mathématiques, Tome 11 (2024), pp. 875-908. doi: 10.5802/jep.268

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