On the Geometric Zilber-Pink Theorem and the Lawrence-Venkatesh method
Gregorio Baldi, Bruno Klingler, and Emmanuel Ullmo
TL;DR
This paper advances the understanding of the Zilber-Pink conjecture by leveraging recent algebraicity results on the Hodge locus, improving Lawrence-Venkatesh's approach towards the refined Bombieri-Lang conjecture.
Contribution
It introduces new algebraicity results for the Hodge locus and applies them to enhance the Lawrence-Venkatesh method related to the Zilber-Pink conjecture.
Findings
Improved bounds towards the Bombieri-Lang conjecture.
New algebraicity results for the Hodge locus of high-level variations.
Enhanced techniques for approaching the Zilber-Pink conjecture.
Abstract
Using our recent results on the algebraicity of the Hodge locus for variations of Hodge structures of level at least , we improve the results of Lawrence-Venkatesh in direction of the refined Bombieri-Lang conjecture.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Analytic Number Theory Research