论文标题
A. Gabrielov定理的证明
A proof of A. Gabrielov's rank Theorem
论文作者
论文摘要
本文包含了加布里埃洛夫（Gabrielov）等级定理的完整证明，这是分析图细菌研究的基本结果。受Gabrielov和Tougeron的作品的启发，我们开发了正式的几何技术，这些技术阐明了原始证明的困难部分。这些技术具有独立的兴趣，我们通过添加了Abhyankar-Jung定理的新（非常简短）证明这一点。此外，我们将级别定理的新扩展（涉及Zariski Main定理和消除理论）和交换代数。
This article contains a complete proof of Gabrielov's rank Theorem, a fundamental result in the study of analytic map germs. Inspired by the works of Gabrielov and Tougeron, we develop formal-geometric techniques which clarify the difficult parts of the original proof. These techniques are of independent interest, and we illustrate this by adding a new (very short) proof of the Abhyankar-Jung Theorem. We include, furthermore, new extensions of the rank Theorem (concerning the Zariski main Theorem and elimination theory) to commutative algebra.
