We study the height of polynomials and derive some important tools.

We prove the celebrated Hensel's lemma using the so-called Newton's method and "double induction", and try to find solutions of polynomials in $\mathbb{Q}_p$.

We give a quick look at the Segre embedding and try to use that in a fundamental tool of Diophantine Geometry - heights.

In this post, we develop a fundamental device: absolute value on an arbitrary field with various points of view.