Fun with Mac Lane valuations

Algebra Seminar
Monday, February 11, 2019 - 1:00pm for 1 hour (actually 50 minutes)
Skiles 005
Andrew Obus – Baruch College, CUNY – Andrew.Obus@baruch.cuny.edu
Padmavathi Srinivasan
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, as well as for proving conductor-discriminant inequalities for higher genus curves. The first project is joint work with Stefan Wewers, and the second is joint work with Padmavathi Srinivasan.