CORDIS Project
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This project focuses on advancing techniques for local uniformization in algebraic geometry. It aims to refine existing theorems related to alterations of integral schemes, particularly in mixed characteristic cases, enhancing the understanding of valuation lifting in these contexts.
Gabber recently proved a weak local uniformization theorem that states that forany quasi-excellent integral scheme X with a valuation v there exists an alterationY->X (i.e. a proper generically finite morphism between integral schemes) suchthat v lifts to a valuation on Y with a regular center.
Moreover, one can achieve thatthe degree of the field extension k(Y)/k(X) is coprime with a fixed prime number linvertible on X.
My recent inseparable local uniformization theorem refines thiswhen X is a…
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