Model theory of special subvarieties and Schanuel-type conjectures
Boris Zilber
TL;DR
This paper employs model theory to redefine and clarify the concept of special subvarieties in Shimura varieties, aiming to deepen the understanding of their structure and properties.
Contribution
It introduces a model-theoretic framework for special subvarieties, providing new insights and potential approaches to Schanuel-type conjectures.
Findings
A new model-theoretic characterization of special subvarieties
Clarification of the structure of special subvarieties in Shimura varieties
Potential implications for Schanuel-type conjectures
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).
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology