Noncommutative Main Conjectures of Geometric Iwasawa Theory

Abstract

We give a survey on noncommutative main conjectures of Iwasawa theory in a geometric setting, i.e. for separated schemes of finite type over a finite field, as stated and proved by Burns and the author. We will also comment briefly on versions of the main conjecture for function fields.

Notes from the "Instructional workshop on the noncommutative main conjectures" held in Münster, April 26 - 30, 2011, http://wwwmath.uni-muenster.de/u/schneider/Workshop_2011/index.html. Changes according to the suggestions of the referee, in particular, correcting the statement of Prop. 2.4 and adding more details to its proof. Accepted for publication in a Springer PROM volume