Complex and p-adic geometric versions of the Schneider-Lang theorem
speaker: Mathilde Herblot (Université Paris Diderot)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 talk, I will give geometrical generalizations of this criterion, holding for both the field of complex numbers and a p-adic field. In dimension one I will state a theorem for formal subschemes admitting a uniformization by an algebraic affine curve. In the higher dimensional case, I will give a theorem which 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.
timetable:
Fri 12 Oct, 11:20 - 12:00, Sala Conferenze Centro De Giorgi
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