A proof of A. Gabrielov's rank Theorem
| Autor: | da Silva, André Belotto, Curmi, Octave, Rond, Guillaume |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Final version, 62 pages, to appear in J. Ec. polytech. Math |
| Databáze: | arXiv |
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