关于极大序模的同余曲面的亏格
On the genus of congruence surfaces from maximal orders
摘要：
本文研究了Breuillard和Reid关于哪些亏格可以由闭同余曲面得到的一个问题。具体地说，我们研究了一个较小的对象，即封闭的同余曲面，可以通过一个极大序模在四元数代数，并证明了没有曲面的亏格212在这一类。特别是，我们表明，Breuillard和里德的问题限制在这样的表面有一个否定的答案。
英文摘要：
In this paper, we investigate a question of Breuillard and Reid concerning which genera can be obtained by closed congruence surfaces. Specifically, we study a smaller set of objects, namely the closed congruence surfaces which can be constructed by a maximal order in a quaternion algebra, and show that there is no surface of genus 212 in this class. In particular, we show that Breuillard and Reid's question restricted to such surfaces has a negative answer.
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