论文标题
Schanuel猜想和应用的半阿伯式类似物
Semi-abelian analogues of Schanuel Conjecture and applications
论文作者
论文摘要
在本文中，我们研究了雪泽猜想的半阿伯式类似物。正如第一作者所表明的那样，雪纳尔的猜想等同于适用于没有阿贝利亚部分的1摩托物的广义时期。扩展了她的方法，第二，第三和第四作者引入了沙内尔猜想的阿贝尔类似物，因为广义时期的猜想适用于没有复曲面部分的1-动物。作为本文的第一个结果，我们将Schanuel猜想的半亚伯利亚类似物定义为适用于1-动力的广义时期的猜想。 C. Cheng等。事实证明，雪纳尔的猜想意味着迭代指数值和迭代对数的价值的代数独立性，回答了M. Waldschmidt的问题。第二名，第三和第四作者在阿贝尔品种的设置中研究了一个类似的问题：弱的阿贝尔·舍诺尔的猜想意味着迭代的阿贝尔指数值的代数独立性和迭代的迭代的广义亚伯利亚对数的值。本文的主要结果是，相对的半阿贝尔猜想意味着迭代的半亚伯指数值的代数独立性和迭代的迭代广义半阿伯式对数的值。
In this article we study Semi-abelian analogues of Schanuel conjecture. As showed by the first author, Schanuel Conjecture is equivalent to the Generalized Period Conjecture applied to 1-motives without abelian part. Extending her methods, the second, the third and the fourth authors have introduced the Abelian analogue of Schanuel Conjecture as the Generalized Period Conjecture applied to 1-motives without toric part. As a first result of this paper, we define the Semi-abelian analogue of Schanuel Conjecture as the Generalized Period Conjecture applied to 1-motives. C. Cheng et al. proved that Schanuel conjecture implies the algebraic independence of the values of the iterated exponential and the values of the iterated logarithm, answering a question of M. Waldschmidt. The second, the third and the fourth authors have investigated a similar question in the setup of abelian varieties: the Weak Abelian Schanuel conjecture implies the algebraic independence of the values of the iterated abelian exponential and the values of an iterated generalized abelian logarithm. The main result of this paper is that a Relative Semi-abelian conjecture implies the algebraic independence of the values of the iterated semi-abelian exponential and the values of an iterated generalized semi-abelian logarithm.
