In this post we deliver the basic computation of the quadratic reciprocity law and see its importance in algebraic number theory.

In this post we show that the Pontryagin dual group of $\mathbb{Q}_p$ is isomorphic to itself.

In this post we study the canonical Haar measure on $Q_p$, and give a explicit definition just as the Lebesgue measure.

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.