## Notes on Speyer’s paper titled “Some Sums over Irreducible Polynomials”

Let be the set of irreducible polynomials over . Then . The paper lists certain examples of below. These are all expanded as geometric series. As one can see only contribute to the coefficient of in the sum . Why don’t the other irreducible polynomials do the same? This is because these are the onlyContinue reading “Notes on Speyer’s paper titled “Some Sums over Irreducible Polynomials””

## Introduction to Schemes

This is a short introduction to Scheme Theory, as modeled on the article by Brian Lawrence. A variety here is a zero set that can be covered by a finite number of affine varieties. Hence, a morphism between varieties can be considered to be a bunch of affine morphisms, as long as they agree onContinue reading “Introduction to Schemes”

## Puiseux Series and Tropical Varieties

Puiseux series- This field is denoted by . Note that we have a double brace “[[ ]]” instead of “[]”. This implies that we have infinite series instead of finite ones (which would be polynomials). The Puiseux laurent series is denoted as . This means that is also allowed to have negative powers. Now ,Continue reading “Puiseux Series and Tropical Varieties”