Algebra/Number Theory Seminar

Formal normal forms and wildly ramified power series

Jonas Nordqvist, Linnaeus University

Friday, April 19th, 2024
12:00 PM - 1:00 PM
Hylan 1106A

In this talk, we investigate power series, fixing the origin, where it is tangent to the identity defined over fields of positive characteristic. While the normal form \(z(1 + z^q + \alpha z^{2q})\) characterizes the formal conjugation of such series in the complex domain, we address the differences that arise in positive characteristic fields. Our primary contribution is the introduction of an invariant under change of coordinates we call the ‘second residue fixed point index’. This invariant is an obstruction for normal forms as described over the complex numbers, and leads to interesting questions about the existence of formal normal forms in positive characteristic.

Event contact: thomas dot tucker at rochester dot edu