On a Newton polygon approach to the uniformization of singularities of characteristic \(p\). (English) Zbl 0876.14002
Campillo López, Antonio (ed.) et al., Algebraic geometry and singularities. Proceedings of the 3rd international conference on algebraic geometry held at La Rábida, Spain, December 9-14, 1991. Basel: Birkhäuser. Prog. Math. 134, 49-93 (1996).
This is a report about some results on uniformization of singularities in characteristic \(p\). Given any singularity defined by the equation: \(T^p-f (x,y,z)=0\) there is a number \(n\) such that along any valuation, the multiplicity will be smaller in \(n\) steps of blow-ups. The main tool is the Newton polygon. The same equation was studied by V. Cossart in his Ph. D. thesis (Orsay 1987) and probably the proof of canonical uniformization in characteristic \(p\) announced by Spivakovsky works in this case, too.
For the entire collection see [Zbl 0832.00033].
For the entire collection see [Zbl 0832.00033].
Reviewer: Dorin-Mihail Popescu (Bucureşti)
MSC:
| 14B05 | Singularities in algebraic geometry |
| 14E15 | Global theory and resolution of singularities (algebro-geometric aspects) |
| 13F30 | Valuation rings |
| 13A35 | Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure |
