Model theory of special subvarieties and Schanuel-type conjectures

2015/01/14 by Boris Zilber, Zilber, Boris · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1501.03301

openalex publication_date 2015/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the language and tools available in model theory to redefine and clarify the rather involved notion of a \em special subvariety known from the theory of Shimura varieties (mixed and pure).

Citations

• A Mordell-Weil theorem for abelian varieties over fields generated by torsion points
• EXPONENTIAL SUMS EQUATIONS AND THE SCHANUEL CONJECTURE
• Categoricity of the two sorted j-function

Cited by

• A conjecture in Schanuel style for 1-motives

Related

• Subvarieties of Shimura varieties
• Local models of Shimura varieties and a conjecture of Kottwitz
• Shimura varieties
• Good Reductions of Shimura Varieties of Hodge Type in Arbitrary Unramified Mixed Characteristic, Part II
• On Special Subvarieties of Kuga Varieties