Residue field

Imagine you have a big apple and you want to cut it into smaller pieces. When you cut the apple, each piece has its own little part of the apple to itself. That little part is called a residue.

Now, imagine you have a big math problem and you want to simplify it. One way to simplify it is to look at the numbers that are left after you divide by a certain number. Those leftover numbers are called the residue numbers.

In algebraic geometry, we like to talk about shapes called algebraic varieties. These shapes are made up of solutions to equations.

But sometimes we want to focus on just one point on the shape. At that point, we can look at all the equations that the point satisfies and use those to make a new shape. This new shape is called the residue field.

The residue field is like a little piece of the original shape, just like the apple pieces before. And just like how we can study the properties of the apple pieces, we can study the properties of the residue field.