Mac Lane valuations and an application to resolution of quotient singularities

Abstract: Mac Lane's technique of "inductive valuations" is over 80 years old, but has only recently been used to attack problems about arithmetic surfaces. We will give an explicit, hands-on introduction to the theory, requiring little background beyond the definition of a non-archimedean valuation.

We will then outline how this theory is helpful for resolving "weak wild" quotient singularities of arithmetic surfaces, a class of singularity studied by Lorenzini that shows up naturally when computing models of curves with potentially good reduction.

Slides.

algebraic geometrynumber theory

Audience: researchers in the discipline

( paper | slides )

VIASM Arithmetic Geometry Online Seminar