Applications of the hyperbolic Ax–Schanuel conjecture

DOI10.1112/S0010437X1800725XzbMath1427.11057arXiv1703.08967WikidataQ122894702 ScholiaQ122894702MaRDI QIDQ3121282

Christopher Daw, Jinbo Ren

Publication date: 15 March 2019

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

Full work available at URL: https://arxiv.org/abs/1703.08967

zbMATH Keywords

Shimura varietiesZilber-Pink conjecturehyperbolic Ax-Schanuel conjecture

Mathematics Subject Classification ID

Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35)

Related Items (24)

Unlikely Intersections with ExCM curves in A2 ⋮ Sets of special subvarieties of bounded degree ⋮ Independence of CM points in elliptic curves ⋮ Weak modular Zilber-Pink with derivatives ⋮ Unlikely intersections with Hecke translates of a special subvariety ⋮ Hodge theory, between algebraicity and transcendence ⋮ The Ax-Schanuel conjecture for variations of mixed Hodge structures ⋮ A note on unlikely intersections in Shimura varieties ⋮ Lattices with skew-Hermitian forms over division algebras and unlikely intersections ⋮ On the distribution of the Hodge locus ⋮ Ax-Lindemann-Weierstrass with derivatives and the genus 0 Fuchsian groups ⋮ Mixed Ax–Schanuel for the universal abelian varieties and some applications ⋮ Generic rank of Betti map and unlikely intersections ⋮ Adequate predimension inequalities in differential fields ⋮ Conjugation of semisimple subgroups over real number fields of bounded degree ⋮ Ax-Schanuel and strong minimality for the \(j\)-function ⋮ Ax-Schanuel for Shimura varieties ⋮ Effective estimates for the degrees of maximal special subvarieties ⋮ Some remarks on atypical intersections ⋮ On CM points away from the Torelli locus ⋮ Ax-Schanuel type theorems on functional transcendence via Nevanlinna theory ⋮ GALOIS CONJUGATES OF SPECIAL POINTS AND SPECIAL SUBVARIETIES IN SHIMURA VARIETIES ⋮ Differential existential closedness for the 𝑗-function ⋮ Special subvarieties of non-arithmetic ball quotients and Hodge theory

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