## Algebraic Function Fields of Genus 0

##### By behackl, 24th May 2015

$\def\mcal#1{\mathcal{#1}} \def\Z{\mathbb{Z}} \def\P{\mathbb{P}} \DeclareMathOperator{\Div}{Div} \def\R{\mathbb{R}}$In this post I want to discuss the exercises from our Algebraic Curves course I worked on (and struggled with) last week.

So, first of all: unfortunately, this post will not be entirely self-containing. There are quite a few statements upon which the statement I write about is build upon — some of which I will explain in more detail, while others will only be stated briefly or even only referenced to. However, except for the characterization which this post is about, there will be no “rigorous” proofs. For a more detailed explanation and for proofs of these statements consult Stichtenoth’s book “Algebraic Function Fields and Codes” (which features the same [or at least a similar] notation as this posting).