论文标题
O_N用于估值戒指的扭曲同源性稳定性
Twisted homology stability of O_n for valuation rings
论文作者
论文摘要
在本文中，我们扩展了Vogtmann的论点，以显示欧几里得正交组$ o_n（a）$的同源稳定性时，当$ a $是其残留物或商字段的算术条件的估值环时。特别是，如果$ a $是Henselian评估戒指，那么如果$ a $的残留场$ a $具有有限的毕达哥拉斯号码，则$ o_n（a）$表现同源稳定性。我们的结果包括Vogtmann的结果，并具有各种扭曲的系数。使用这些结果，我们为剪刀一致性研究中某些计算的字段提供了类似物。
In this article, we extend an argument of Vogtmann in order to show homology stability of the Euclidean orthogonal group $O_n(A)$ when $A$ is a valuation ring subject to arithmetic conditions on either its residue or its quotient field. In particular, it is shown that if $A$ is a henselian valuation ring, then the groups $O_n(A)$ exhibit homology stability if the residue field of $A$ has finite Pythagoras number. Our results include those of Vogtmann, and hold with various twisted coefficients. Using these results, we give analogues for fields $F\neq\mathbb R$ of some computations that appear in the study of scissor congruences.
