Fun with Mac Lane valuations

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 useful for resolving "weak wild" quotient singularities of arithmetic surfaces (joint with Stefan Wewers), proving conductor-discriminant inequalities for hyperelliptic and superelliptic curves (joint with Padmavathi Srinivasan), and understanding regular models of potentially Mumford curves (joint with Daniele Turchetti).

number theory

Audience: researchers in the topic

Heilbronn number theory seminar

Series comments: This is part of the University of Bristol's Heilbronn number theory seminar. If you wish to attend the talk (and are not a Bristolian), please register using this form or email us at bristolhnts@gmail.com with your name and affiliation (if any).

We will email out the link to all registered participants the day before.