A uniform construction of smooth integral models and a conjectural recipe for computing local densities
A uniform construction of smooth integral models and a conjectural recipe for computing local densities
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光滑积分模型的统一构造和计算局部密度的推测方法
DOI：
10.1093/imrn/rnw340
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
S. Cho
中科院分区：
文献类型：
--
作者：
Hossain MA;Mahmud M;Malek MA and Sawada Y.;S. Cho
在这篇文章中，我们解释了一个简单而统一的光滑积分模型的构造，该模型与定义在任意局部域上的二次格、（反）厄米格和（反）四元格厄米格相关。作为一个主要的应用，我们通过引入一个关于光滑积分模型的特殊纤维的有理点的个数的猜想，解释了一个计算局部密度的猜想配方，这是在数域的整数环上的上述形式分类的一个重要因素。
In this article, we explain a simple and uniform construction of a smooth integral model associated to a quadratic, (anti)-hermitian, and (anti)-quaternionic hermitian lattice defined over an arbitrary local field. As one major application, we explain a conjectural recipe for computing local densities case by case, which is an essential factor in the classification of forms as above over the ring of integers of a number field, by introducing one conjecture about the number of rational points of the special fiber of a smooth integral model.