## Exercise concerning quaternion algebras

Here’s a fun problem that came up in a talk by Jacob Tsimerman on Monday concerning some joint work with Andrew Snowden:

Problem: Let $D/\mathbf{Q}(t)$ be a quaternion algebra such that the specialization $D_t$ splits for almost all $t$. Then show that $D$ itself is split.

As a comparison, if you replace $\mathbf{Q}$ by $\overline{\mathbf{Q}}$, then although the condition that $D_t$ splits becomes empty, the conclusion is still true, by Tsen’s theorem.

This definitely *feels* like the type of question which should have a slick solution; can you find one?