论文标题
算术表面的终端订单
Terminal orders on arithmetic surfaces
论文作者
论文摘要
算术表面上末端brauer类的局部结构分类为[CI21]在[CI05]中进行的几何表面上的分类。对这些分类的一部分兴趣是，它使最小模型程序可以应用于表面上订单的非交通设置。在本文中，至少在程度为质量p> 5时，我们为算术表面上的末端订单提供了局部结构定理。这概括了几何情况下给出的结构定理。它们都可以明确构造为符号上的矩阵代数。从这个描述中，人们可以看到，这种终端订单都具有全球尺寸二，因此概括了终端（交换）表面光滑且因此具有同源性的事实。
The local structure of terminal Brauer classes on arithmetic surfaces were classified in [CI21] generalising the classification on geometric surfaces carried out in [CI05]. Part of the interest in these classifications is that it enables the minimal model program to be applied to the noncommutative setting of orders on surfaces. In this paper, we give etale local structure theorems for terminal orders on arithemtic surfaces, at least when the degree is a prime p >5. This generalises the structure theorem given in the geometric case. They can all be explicitly constructed as algebras of matrices over symbols. From this description one sees that such terminal orders all have global dimension two, thus generalising the fact that terminal (commutative) surfaces are smooth and hence homologically regular.
