Valuation theoretic and model theoretic aspects of local uniformization. (English) Zbl 1046.14001
Hauser, H. (ed.) et al., Resolution of singularities. A research textbook in tribute to Oscar Zariski. Based on the courses given at the working week in Obergurgl, Austria, September 7–14, 1997. Basel: Birkhäuser (ISBN 3-7643-6178-6/hbk). Prog. Math. 181, 381-456 (2000).
This is a global survey on local uniformization. To cite the author: “In this paper, I will take you on an excursion from algebraic geometry through valuation theory to model theoretic algebra, and back. If our destination sounds too exotic for you, you may jump off at the Old World (valuation theory) and divert yourself with problems and examples until you catch our plane back home.” The paper consists of 23 chapters and states finally 18 open problems.
For the entire collection see [Zbl 0932.00042].
For the entire collection see [Zbl 0932.00042].
MSC:
| 14B05 | Singularities in algebraic geometry |
| 13A18 | Valuations and their generalizations for commutative rings |
| 14E22 | Ramification problems in algebraic geometry |
| 03C60 | Model-theoretic algebra |
