The Hyperbolic Ax-Lindemann-Weierstrass conjecture

2013/07/15 by Bruno Klingler, Klingler, Bruno, Emmanuel Ullmo +3 · 3 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1307.3965

openalex publication_date 2013/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The hyperbolic Ax-Lindemann-Weierstrass conjecture is a functional algebraic independence statement for the uniformizing map of an arithmetic variety. In this paper we provide a proof of this conjecture, generalizing previous work of Pila-Tsimerman and Peterzil-Starchenko.

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