混合周期映射导数的 Ax-Schanuel 定理

The Ax-Schanuel conjecture for variations of mixed Hodge structures

We prove in this paper the Ax-Schanuel conjecture for all admissible variations of mixed Hodge structures.

Mixed Ax-Schanuel for the universal abelian varieties and some applications

In this paper we prove the mixed Ax-Schanuel theorem for the universal abelian varieties (more generally any mixed Shimura variety of Kuga type), and give some simple applications. In particular we present an application to studying the generic rank of the Betti map.

混合霍奇结构变分的Ax-Schanuel定理

Ax-Schanuel for variations of mixed Hodge structures

该研究给出混合弱Mumford-Tate域实分裂收缩的性质，证明混合霍奇结构变分的周期映射的Ax-Schanuel性质，创新点在于点计数步骤采用可定义商上的有理点计数。

Ax-Schanuel 的微分方法，I

A differential approach to Ax-Schanuel, I

本文利用微分几何、微分代数与微分闭域模型论的工具，证明了关于几何结构均匀化子的多个 Ax-Schanuel 型结果，包括带有导数的完整 Ax-Schanuel 定理以及 j-函数与指数函数导数的强 Ax-Schanuel 结果。

Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results

We develop a theory of enlarged mixed Shimura varieties, putting the universal vectorial bi-extension defined by Coleman into this framework to study some functional transcendental results of Ax type. We study their bi-algebraic systems, formulate the Ax-Schanuel conjecture and explain its relation with the Ax logarithmique theorem and the Ax-Lindemann theorem which we shall prove. We also prove the whole Ax-Schanuel conjecture for the unipotent part. All these bi-algebraic and transcendental results generalize their counterparts for mixed Shimura varieties. In the end we briefly discuss about…

周期的函数超越性与几何 André–Grothendieck 周期猜想

Functional Transcendence of Periods and the Geometric André--Grothendieck Period Conjecture

本文通过证明代数簇族中代数形式积分的函数超越性，给出混合 Hodge 结构变分的 Ax–Schanuel 结果，并据此建立几何形式的 André–Grothendieck 周期猜想。