CSUN Algebra, Number Theory, and Discrete Mathematics Seminar

We will begin by discussing covers of curves in characteristic zero and characteristic $p>0$, focusing in characteristic $p$ on curves that can be viewed as both an Artin-Schreier cover of the affine line and a Kummer cover of the punctured affine line. This will lead us to the algebraic fundamental group (a profinite group). We will see how results related to the “lower levels” of this group, impact the structure of the fundamental group as a whole.