Definability of restricted theta functions and families of abelian varieties

DOI10.1215/00127094-2080018zbMath1284.03215arXiv1103.3110OpenAlexW3102793388MaRDI QIDQ1949160

Yaa'cov Peterzil, Sergei Starchenko

Publication date: 25 April 2013

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.3110

zbMATH Keywords

o-minimalityAndré-Oort conjectureSiegel modular varieties

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Theta functions and abelian varieties (14K25) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35) Applications of model theory (03C98) Model theory of ordered structures; o-minimality (03C64)

Related Items (24)

Wilkie's conjecture for restricted elementary functions ⋮ The hyperbolic Ax-Lindemann-Weierstraß conjecture ⋮ Independence of CM points in elliptic curves ⋮ Global complexification of real analytic globally subanalytic functions ⋮ Algebraic differential equations from covering maps ⋮ Towards the André-Oort conjecture for mixed Shimura varieties: the Ax-Lindemann theorem and lower bounds for Galois orbits of special points ⋮ Tameness in geometry and arithmetic: beyond o-minimality ⋮ Hodge theory, between algebraicity and transcendence ⋮ The André-Oort conjecture for \(\mathcal A_g\) ⋮ Locally definable subgroups of semialgebraic groups ⋮ \(o\)-minimality and the André-Oort conjecture for \(\mathbb{C}^{n}\) ⋮ Hyperbolic Ax-Lindemann theorem in the cocompact case ⋮ ENLARGED MIXED SHIMURA VARIETIES, BI-ALGEBRAIC SYSTEM AND SOME AX TYPE TRANSCENDENTAL RESULTS ⋮ Ax-Lindemann-Weierstrass with derivatives and the genus 0 Fuchsian groups ⋮ Ax-Lindemann for \(\mathcal{A}_g\) ⋮ Tame topology of arithmetic quotients and algebraicity of Hodge loci ⋮ Analytic continuations of log-exp-analytic germs ⋮ Mixed Ax–Schanuel for the universal abelian varieties and some applications ⋮ Effective André-Oort conjecture for non-compact curves in Hilbert modular varieties ⋮ Ax-Schanuel for Shimura varieties ⋮ Unlikely intersections between isogeny orbits and curves ⋮ Model Completeness for the Real Field with the Weierstrass ℘ Function ⋮ An application of Cartan's equivalence method to Hirschowitz's conjecture on the formal principle ⋮ Counting special points: Logic, diophantine geometry, and transcendence theory

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