Ax-Schanuel with derivatives for mixed period mappings

TL;DR

This paper establishes the Ax-Schanuel property for derivatives of mixed period mappings, extending the understanding of their algebraic and transcendental relations, with implications for complex geometry and number theory.

Contribution

It proves the Ax-Schanuel property for derivatives of mixed period mappings and provides a jet space reformulation, building on prior Ax-Schanuel results for principal bundles.

Findings

Proved Ax-Schanuel property for derivatives of mixed period mappings

Established jet space reformulation of the Ax-Schanuel result

Extended the application of Ax-Schanuel to complex geometric structures

Abstract

We prove the Ax-Schanuel property of the derivatives of mixed period mappings. We also prove the jet space reformulation of this result. The proofs use the Ax-Schanuel result for principal bundles with flat connections obtained by Bl\'{a}zquez-Sanz, Casale, Freitag, and Nagloo.