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The Modular Perspective

Mathematics for Budding Mathematicians

Number Theory

Understanding Varieties

April 15, 2020November 30, 2020Henry TwissLeave a comment

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.

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Geometry, Number Theory

The Arithmetic of Polynomial Rings over Finite Fields

February 25, 2019April 11, 2020Henry TwissLeave a comment

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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Algebra, Number Theory
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