In a 2012 note in Comptes Rendus Mathématique, the author did try to answer a question of Jean-Pierre Serre; it has recently been announced that the scope of that answer needs an adjustment, and the details of this adjustment are given in the present paper. The original question is the following. Consider the ring of integers \(\mathcal {O}\) in an imaginary quadratic number field, and the Borel–Serre compactification of the quotient of hyperbolic 3–space by \(\mathrm {SL_2}(\mathcal {O})\). Consider the map \(\alpha \) induced on homology when attaching the boundary into the Borel–Serre compactification. How can one determine the kernel of \(\alpha \)(in degree 1) ? Serre used a global topological argument and obtained the rank of the kernel of \(\alpha \). He added the question what submodule precisely this kernel is.

在2012年Comptes RendusMathématique的注释中，作者确实试图回答Jean-Pierre Serre的问题。最近宣布，该答案的范围需要调整，此调整的详细信息在本文中给出。原始问题如下。考虑虚数二次域中的整数\（\ mathcal {O} \）环 ，并用\（\ mathrm {SL_2}（\ mathcal {O}）对双曲3空间商进行Borel-Serre压缩\）。当将边界附加到Borel-Serre压实中时，考虑在同源性上引起的映射 \（\ alpha \）。如何确定 \（\ alpha \）的内核（以度1为单位）？Serre使用了全局拓扑参数，并获得了\（\ alpha \）的内核等级 。他添加了一个问题，即该内核究竟是什么子模块。