The Theorem of the Base

The Theorem of the Base states that the Neron-Severi group, the group of line bundles on a proper variety modulo algebraic equivalence, is finitely generated, and that the group of line bundles modulo numerical equivalence is equal to Neron-Severi modulo torsion. I will discuss the proof, focusing on the finiteness of the torsion and why numerically trivial line bundles are torsion in the Neron-Severi group.