Varieties are a basic structure in algebraic geometry. They were the central objects of study before Grothendieck reinvented the entire theory in his treatise *Éléments de géométrie algébrique* by introducing schemes. In the following we will introduce varieties and define algebraic curves.

# Number Theory

## The Arithmetic of Polynomial Rings over Finite Fields

We’re going to discuss the arithmetic of polynomial rings over finite fields and its similarity to the arithmetic of the integers. We’ll first run though some preliminary observations about the arithmetic of polynomial rings which will suggest that it behaves similar to the arithmetic of the integers.

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