Birational Nevanlinna Constants, Beta Constants, and Diophantine Approximation to Closed Subschemes

Vojta, Paul

Journal de théorie des nombres de Bordeaux, Tome 35 (2023) no. 1, pp. 17-61

In an earlier paper (joint with Min Ru), we proved a result on diophantine approximation to Cartier divisors, extending a 2011 result of P. Autissier. This was recently extended to certain closed subschemes (in place of divisors) by Ru and Wang. In this paper we extend this result to a broader class of closed subschemes. We also show that some notions of $\beta (ℒ,D)$ coincide, and that they can all be evaluated as limits.

Dans un article antérieur (en commun avec Min Ru), nous avons prouvé un résultat sur l’approximation diophantienne relativement aux diviseurs de Cartier, en généralisant un résultat de 2011 de P. Autissier. Cela a été récemment étendu à certains sous-schémas fermés (à la place de diviseurs) par Ru et Wang. Dans cet article, nous étendons ce résultat à une classe de sous-schémas fermés plus large. Nous montrons également que certaines notions de $\beta (ℒ,D)$ coïncident, et qu’elles peuvent toutes être évaluées comme des limites.

Classification : 11J97, 32H30
Keywords: Nevanlinna constant, b-divisors, closed subscheme

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