NTS ABSTRACT
Return to NTS Fall 2015
Sep 03
Kiran Kedlaya |
On the algebraicity of (generalized) power series |
A remarkable theorem of Christol from 1979 gives a criterion for detecting whether a power series over a finite field of characteristic p represents an algebraic function: this happens if and only if the coefficient of the n-th power of the series variable can be extracted from the base-p expansion of n using a finite automaton. We will describe a result that extends this result in two directions: we allow an arbitrary field of characteristic p, and we allow "generalized power series" in the sense of Hahn-Mal'cev-Neumann. In particular, this gives a concrete description of an algebraic closure of a rational function field in characteristic p (and corrects a mistake in my previous attempt to give this description some 15 years ago). |
Sep 10
Sean Rostami |
Fixers of Stable Functionals |
Coming soon... |