Determining potential good reduction in arithmetic dynamics
Speaker:
Rob Benedetto, Amherst College
Date and Time:
Friday, July 29, 2016 - 11:00am to 12:00pm
Location:
Fields Institute, Room 230
Abstract:
Let K be a non-archimedean field, and let φ(z) ∈ K(z) be a rational function. In 1994, Morton and Silverman defined the notions of good and bad reduction of φ. It is then natural to define φ to have potential good reduction if it is conjugate, possibly over a larger field L/K, to a map of good reduction. In this talk we discuss a simple criterion for determining whether or not φ has potential good reduction. We also consider how large an extension L/K may be required to exhibit good reduction.