Fun with Mac Lane valuations

Series: 
Algebra Seminar
Monday, February 11, 2019 - 1:00pm
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Baruch College, CUNY
,  
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.