Is there a proof for this theorem?
$Theorem$: Let $\mathbb F_q$ be a finite field of order $q$ = $p^n$, and let $C$ be an absolutely irreducible smooth projective curve defined over $\mathbb F_q$. To each such curve $C$ one can associate a genus $g$; for instance, elliptic curves have genus $1$. We can also count the cardinality $|C({\mathbb F}_q)|$ of the set $C({\mathbb F}_q)$ of ${\mathbb F}_q$-points of $C$. We now state the Hasse-Weil bound: $\left|\,|C(\mathbb F_q)|-q-1\,\right|\leq 2g\,q^{1/2}$.
I tried reading the proof Terence Tao left on his blog, but I seem quite stumped. Is there a link for a more simple proof, or something more understandable?