Holomorphic curves in mixed Shimura varieties

TL;DR

This paper extends the Bloch-Ochiai theorem to mixed Shimura varieties, leveraging prior results and the Ax-Lindemann-Weierstrass theorem to advance understanding of holomorphic curves in these complex algebraic structures.

Contribution

It introduces an analogue of the Bloch-Ochiai theorem for mixed Shimura varieties, building on previous work and key theorems in the field.

Findings

Proved an analogue of the Bloch-Ochiai theorem for mixed Shimura varieties.

Utilized the Ax-Lindemann-Weierstrass theorem in the context of mixed Shimura varieties.

Extended the theoretical framework for holomorphic curves in complex algebraic varieties.

Abstract

Following work by Ullmo and Yafaev, we propose and prove an analogue of the Bloch-Ochiai theorem in the context of mixed Shimura varieties. We follow the strategy and use results of previous articles by Ullmo and Yafaev and the author plus consequences of the Ax-Lindemann-Weierstrass theorem for mixed Shimura varieties due to Gao.