论文标题
RISO分类和树不变
Riso-stratifications and a tree invariant
论文作者
论文摘要
我们介绍了一个新的分层概念（````````'riso-stratificate''）了，该概念是规范性的，并且在各种环境中存在，包括$ \ Mathbb {c} $，$ \ Mathbb {r} $和$ \ Mathbb {Q} Q} _p $ nctress od o-minim in $ minim in $ minim in $ nimal in $ minim in $ minim in $ minim in $ minim nim in $ minim in $ n of。直接根据沿着地层的琐事概念直接定义了RISO分类。关键的困难和主要结果是以这种方式定义的地层是``自然界的代数''，即在相应的一阶语言中可以定义。作为示例应用程序，我们表明，在某种意义上，当地的动机庞加莱系列在RISO分层的阶层是微不足道的。 Riso分层的概念的背后是一种新的奇异性不变性，我们称之为``riso-Tree''，并以规范的方式捕获了在Lipschitz分层的非规范地层中包含的信息。在进入Poincaré系列应用程序的途中，我们表明我们的观念与动机融合良好。
We introduce a new notion of stratification (``riso-stratification''), which is canonical and which exists in a variety of settings, including different topological fields like $\mathbb{C}$, $\mathbb{R}$ and $\mathbb{Q}_p$, and also including different o-minimal structures on $\mathbb{R}$. Riso-stratifications are defined directly in terms of a suitable notion of triviality along strata; the key difficulty and main result is that the strata defined in this way are ``algebraic in nature'', i.e., definable in the corresponding first-order language. As an example application, we show that local motivic Poincaré series are, in some sense, trivial along the strata of the riso-stratification. Behind the notion of riso-stratification lies a new invariant of singularities, which we call the ``riso-tree'', and which captures, in a canonical way, information that was contained in the non-canonical strata of a Lipschitz stratification. On our way to the Poincaré series application, we show, among others, that our notions interact well with motivic integration.
