Statistics of Number Fields and Function Fields
Statistics of Number Fields and Function Fields
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数字字段和功能字段统计
DOI：
10.1142/9789814324359_0056
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发表时间：
2011
影响因子：
1.3
通讯作者：
J. Ellenberg
中科院分区：
文献类型：
--
作者：
Akshay Venkateshand;J. Ellenberg
我们讨论算术分布的一些问题，包括Cohen-Lenstra、Malle和Bhargava的猜想；我们解释了如何启发式地理解有限域上的函数域的此类猜想，并讨论基于赫维茨空间拓扑的函数域上下文中证明其证明的一般方法。这种方法还表明，舒尔乘数在此类数字字段问题中发挥着作用。
We discuss some problems of arithmetic distribution, including conjectures of Cohen-Lenstra, Malle, and Bhargava; we explain how such conjectures can be heuristically understood for function fields over finite fields, and discuss a general approach to their proof in the function field context based on the topology of Hurwitz spaces. This approach also suggests that the Schur multiplier plays a role in such questions over number fields.