论文标题
通过功能字段类似物的bruhat-tit树的商类似物
Quotients of the Bruhat-Tits tree by function field analogs of the Hecke congruence subgroups
论文作者
论文摘要
Let C be a smooth, projective and geometrically integral curve defined over a finite field F. For each closed point P of C, let R be the ring of functions that are regular outside P, and let K be the completion at P of the function field of C. In order to study groups of the form GL2(R), Serre describes the quotient graph GL2(R)\t, where t is the Bruhat-Tits tree defined from SL2(K).特别是，Serre表明GL2（r）\ t是有限图和有限数量的射线形子图（称为尖）的结合。不难看到有限索引子组继承了此属性。 在这项工作中，我们描述了相关的商图H \ t用于对GL2（r）中矩阵h组的作用的作用，这些图是上三角模量的矩阵h \ t。更具体地，我们给出了H \ t的尖尖数的明确公式。然后，通过使用低音 - 列理论，我们描述了H的组合结构。这些组在函数字段上下文中扮演的角色与SL2（z）的Hecke一致性亚组相同。
Let C be a smooth, projective and geometrically integral curve defined over a finite field F. For each closed point P of C, let R be the ring of functions that are regular outside P, and let K be the completion at P of the function field of C. In order to study groups of the form GL2(R), Serre describes the quotient graph GL2(R)\t, where t is the Bruhat-Tits tree defined from SL2(K). In particular, Serre shows that GL2(R)\t is the union of a finite graph and a finite number of ray shaped subgraphs, which are called cusps. It is not hard to see that finite index subgroups inherit this property. In this work we describe the associated quotient graph H\t for the action on t of the group H of matrices in GL2(R) that are upper triangular modulo a certain ideal I of R. More specifically, we give a explicit formula for the cusp number of H\t. Then, by using Bass-Serre Theory, we describe the combinatorial structure of H. These groups play, in the function field context, the same role as the Hecke congruence subgroups of SL2(Z).
