### Fun with Mac Lane valuations

Heilbronn Number Theory Seminar

24th February 2021, 4:00 pm – 5:00 pm

Zoom,

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).

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