TITLE: Factorization of primes and $Spec(\mathcal{O}_K)$
QUESTION [6 upvotes]: Let $K$ be a quadratic number field, and $\mathcal{O}_K$ the ring of integers of $K$.
The map $\pi: Spec(\mathcal{O}_K) \rightarrow Spec(\mathbb{Z})$ that sends a prime ideal $\mathbb{p}$ to $\mathbb{p} \cap \mathbb{Z}$ is induced since $\mathcal{O}_K$ contains $\mathbb{Z}$. And the fiber $\pi^{-1}$ of the prime ideal $(p)$ of $\mathbb{Z}$ is then understood as the decomposition of $(p)$ in $\mathcal{O}_K$.
We then obtain a geometric interpretation of how p factors in $\mathcal{O}_K$ using results obtained from Algebraic number theory. 
I'm looking for hints to (major or minor!) results that can be proved regarding the behaviour of $(p)$ in $\mathcal{O}_K$, or other interesting aspects of $\mathcal{O}_K$ using "as much as possible" Algebraic geometry  (at level of a first course in Schemes, using, say first seven chapters of Liu's "Algebraic Geometry and Arithmetic Curves").
I'd also appreciate a recommendation of a textbook or notes that discusses these ideas in details.

REPLY [4 votes]: As suggested in a comment by Quiaochu Yuan, Neukirch's book is really good, but I'd recommend you to have a look also at the beautiful lecture notes on Arithmetic Geometry by Lucien Szpiro. You can find them in his webpage, here.
These are the notes of a course given by Szpiro in Orsay and they are in French (Cours De Géométrie Arithmétique), but it looks like somebody TeX-ed and translated (alas, just part of) them (Basic Arithmetic Geometry Notes).
Szpiro starts by studying Picard groups and one-dimensional rings and then discusses in a very geometric flavour some classical results of algebraic number theory (finiteness of $Pic$, Dirichlet's unit theorem...).