# Algebra/Number Theory Seminar

## Linearizability of power series over a discrete valuation ring of positive characteristic

Rufei Ren, University of Rochester

Tuesday, September 18th, 2018
3:00 PM - 4:00 PM
Gavett 206

Michael Herman and P-J Yoccoz prove that every power series $f(T)=\lambda T+\sum\limits_{i=2}^\infty a_iT^i \in Q_p[\![T]\!]$ such that $\|\lambda\|=1$ and $\lambda$ is not a root of unity is linearizable. They asked the same question for polynomials over $F_p[\![T]\!]$, a completed discrete valuation ring of positive characteristic.

In this paper, we prove that, on opposite, most such polynomials in this case are more likely to be non-linearizable. More precisely, we give a sufficient condition of a polynomial in this form being linearizable. In particular, we prove that any polynomial of the form $\lambda T+a_2T^2+a_pT^p$ is not linearizable.

Event contact: c dot d dot haessig at rochester dot edu