论文标题
关于Quaternionig刚性杂形cocyles
On quaternionic rigid meromorphic cocyles
论文作者
论文摘要
最近，达尔蒙（Darmon）和冯克（Vonk）启动了组$ \ mathrm {sl} _2（\ mathbb {z} [1/p]）$的刚性meromorphic Cocycles的理论。他们的主要结果之一是与这种共生相关的除数的代数。我们将结果概括为$ \ mathfrak {p} $ - $ \ mathrm {sl} _2 $的内部形式的算术子组，而不是任意数字字段。证明方法与达尔蒙（Darmon）和沃克（Vonk）的一种不同。他们的证明依赖于通过模块化符号和持续的分数对共同体学的明确描述，而我们的主要工具是算术组的Bieri-Eckmann双重性。
Recently, Darmon and Vonk initiated the theory of rigid meromorphic cocycles for the group $\mathrm{SL}_2(\mathbb{Z}[1/p])$. One of their major results is the algebraicity of the divisor associated to such a cocycle. We generalize the result to the setting of $\mathfrak{p}$-arithmetic subgroups of inner forms of $\mathrm{SL}_2$ over arbitrary number fields. The method of proof differs from the one of Darmon and Vonk. Their proof relies on an explicit description of the cohomology via modular symbols and continued fractions, whereas our main tool is Bieri-Eckmann duality for arithmetic groups.
