TITLE: The Picard number of the Kummer surface of an abelian surface
QUESTION [11 upvotes]: Let $A$ be an abelian surface and $\text{Km}(A)$ be the Kummer surface of $A$. If I remember correctly, the Picard number $\rho(\text{Km}(A))$ is equal to $16+\rho(A)$. 

Does anyone know any reference or proof for this fact?

REPLY [6 votes]: I have written up a self-contained proof of this fact. It is available on Thuses. The proof is entirely algebraic, works over any separably closed field of $\text{char} \neq 2$, and does not use any Hodge theory.