# Birch and Swinnerton-Dyer conjecture in positive characteristic

Is the Birch and Swinnerton-Dyer conjecture known in positive characteristic?

However, if you have an elliptic curve $E$ over a finite field $k$ and a function field $K$ of a curve in positive characteristic, then by base change you may consider $E_K$ as a "constant" curve over $K$. In which case I do believe that BSD is known, but hopefully someone else can help me with a precise reference as I cannot remember it.