2 problems

Let $f\colon X\rightarrow C$ be a smooth projective surface fibration over a smooth projective curve over $k=\mathbb{F}_q$, with smooth generic fibre $X_\eta$ over $K=k(C)$, and le…

Let $E$ be an elliptic curve over a global field $K$, and write $\Sha(E/K)$ for its Tate–Shafarevich group. Cassels's conjecture. There should exist a canonical bilinear form … tha…