论文标题
部分可观测时空混沌系统的无模型预测
Milnor-Witt cycle modules over an excellent DVR
论文作者
论文摘要
Milnor-Witt循环模块在[Feld，N。，Milnor-Witt循环模块，纯和应用代数杂志224（2020）106298]中的定义很容易通过一般的常规基础方案进行调整。但是，有一个简单的示例可以表明，如果基座不是字段，则通常对于循环模块而言，Gersten复合物并非确切。本文的目的是表明，对于一类限制的Milnor-Witt循环模块，在一个出色的DVR上满足了一个额外的公理，在此称为R5，Gersten Complex和$ \ Mathbb {a}^a}^1 $ invariance Hold的预期属性。此外，当基数是一个完美的字段时，R5可以空虚地满足，并且在任何基础上也可以通过$ k^{mw} $满足。作为推论，我们在出色的DVR上获得了严格的$ \ mathbb {a}^1 $ invariance和$ k^{mw} $的精确性。
The definition of Milnor-Witt cycle modules in [Feld, N., Milnor-Witt cycle modules, Journal of Pure and Applied Algebra 224 (2020) 106298] can easily be adapted over general regular base schemes. However, there are simple examples to show that Gersten complex fails to be exact for cycle modules in general if the base is not a field. The goal of this article is to show that, for a restricted class of Milnor-Witt cycle modules over an excellent DVR satisfying an extra axiom, called here as R5, the expected properties of exactness of Gersten complex and $\mathbb{A}^1$-invariance hold. Moreover R5 is vacuously satisfied when the base is a perfect field and it is also satisfied by $K^{MW}$ over any base. As a corollary, we obtain the strict $\mathbb{A}^1$-invariance and the exactness of Gersten complex for $K^{MW}$ over an excellent DVR.
