Applications du théorème d’Ax–Lindemann hyperbolique

DOI10.1112/S0010437X13007446zbMath1326.14062MaRDI QIDQ2877485

Emmanuel Ullmo

Publication date: 22 August 2014

Published in: Compositio Mathematica (Search for Journal in Brave)

zbMATH Keywords

Shimura varietieso-minimalityarithmetic geometry

Mathematics Subject Classification ID

Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35) Model theory of ordered structures; o-minimality (03C64)

Related Items (21)

About the mixed André-Oort conjecture: reduction to a lower bound for the pure case ⋮ The hyperbolic Ax-Lindemann-Weierstraß conjecture ⋮ Heights of pre-special points of Shimura varieties ⋮ Holomorphic curves in compact Shimura varieties ⋮ Towards the André-Oort conjecture for mixed Shimura varieties: the Ax-Lindemann theorem and lower bounds for Galois orbits of special points ⋮ Manin-Mumford by Weyl's criterion ⋮ Topological and equidistributional refinement of the André-Pink-Zannier conjecture at finitely many places ⋮ Big Picard theorem for jet differentials and non-Archimedean Ax-Lindemann theorem ⋮ Hodge theory, between algebraicity and transcendence ⋮ On the generalised André-Pink-Zannier conjecture ⋮ Lattices with skew-Hermitian forms over division algebras and unlikely intersections ⋮ On the distribution of the Hodge locus ⋮ Algebraic flows on Shimura varieties ⋮ ANDRÉ–OORT CONJECTURE AND NONVANISHING OF CENTRAL -VALUES OVER HILBERT CLASS FIELDS ⋮ ENLARGED MIXED SHIMURA VARIETIES, BI-ALGEBRAIC SYSTEM AND SOME AX TYPE TRANSCENDENTAL RESULTS ⋮ Ax-Lindemann for \(\mathcal{A}_g\) ⋮ Holomorphic curves in Shimura varieties ⋮ Mixed Ax–Schanuel for the universal abelian varieties and some applications ⋮ An o-minimal characterization of special subvarieties ⋮ Applications of the hyperbolic Ax–Schanuel conjecture ⋮ Special subvarieties of non-arithmetic ball quotients and Hodge theory

Cites Work

• Abelian varieties isogenous to a Jacobian
• \(o\)-minimality and the André-Oort conjecture for \(\mathbb{C}^{n}\)
• Non-divergence of translates of certain algebraic measures
• Rational points in periodic analytic sets and the Manin-Mumford conjecture
• The rational points of a definable set
• A CHARACTERIZATION OF SPECIAL SUBVARIETIES

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