Valuation Theoretic and Model Theoretic Aspects of Local Uniformization

By Franz-Viktor Kuhlmann. 2010

87 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ea55f501b29d32c2a26c5de4b065ca4fc7f0d077

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Steven Dale Cutkosky

Citations in the corpus

The algebra and model theory of tame valued fields (2013, background): “For a survey on a valuation theoretical approach to resolution of singularities and its relation to the model theory of valued fields, see [20].”
Resolution of singularities of threefolds in positive characteristic. I.: Reduction to local uniformization on Artin–Schreier and purely inseparable coverings (2008, unknown): “2 stresses the role played by immediate wildly ramified extensions of valued fields which are the main obstruction to proving local uniformization, see [31] and [33].”
Resolution of Singularities (2004, background): “Prove that X is non-singular, and X is smooth over K at every point except at the prime (yp − t, x).”