Formal classification of Parabolic Maps in Positive Characteristic
Välkommen till föreläsningen i seminarieserien i matematik.
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. In relation to this, we discuss some new results and conjuectures on the topic.