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Sur le théorème de Schneider-Lang

Abstract : The Schneider-Lang theorem is a classic transcendence criterion for complex numbers. It asserts that there are only finitely many points at which algebraically independent meromorphic functions of finite order of growth can simultaneously take values in a number field, when satisfying a polynomial differential equation with coefficients in this given number field. In this Thesis, we prove geometrical generalizations of this criterion, holding for both the field of complex numbers and a p-adic field. These results are based on suitable Schwarz lemmas we have been able to establish. In dimension one we have proven a theorem for formal subschemes admitting a uniformization by an algebraic affine curve. In the higher dimensional case, our theorem applies to formal subschemes with a uniformization by a product of open subsets of the affine line, under the additional hypothesis that the set of rational points is a Cartesian product. The proofs of these results rely on the slopes method developed by J.-B. Bost and make use of the language of Arakelov geometry.
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Contributor : Mathilde Herblot <>
Submitted on : Friday, January 13, 2012 - 1:31:01 PM
Last modification on : Thursday, January 7, 2021 - 4:24:08 PM
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  • HAL Id : tel-00659675, version 1


Mathilde Herblot. Sur le théorème de Schneider-Lang. Théorie des nombres [math.NT]. Université Rennes 1, 2011. Français. ⟨tel-00659675⟩



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