论文标题
排名2吸引者和迪格尼的猜想
Rank-2 attractors and Deligne's conjecture
论文作者
论文摘要
在本文中，我们将研究Rank-2吸引子的算术几何形状，这些几何形状是Calabi-yau的三倍，其Hodge结构可以接受有趣的分裂。我们将开发方法来分析Rank-2吸引子的代数DE RHAM共同体，我们将通过关注Candelas，de la Ossa，Elmi和van Straten最近的一份示例来说明我们的方法如何工作。我们将研究字符串理论中的等级2吸引子与Deligne对$ L $ functions的特殊值的猜想之间的有趣联系。我们还将提出有关字符串理论与数字理论之间潜在联系的几个开放问题。
In this paper, we will study the arithmetic geometry of rank-2 attractors, which are Calabi-Yau threefolds whose Hodge structures admit interesting splits. We will develop methods to analyze the algebraic de Rham cohomologies of rank-2 attractors, and we will illustrate how our methods work by focusing on an example in a recent paper by Candelas, de la Ossa, Elmi and van Straten. We will look at the interesting connections between rank-2 attractors in string theory and Deligne's conjecture on the special values of $L$-functions. We will also formulate several open questions concerning the potential connections between string theory and number theory.
