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 be a quaternion algebra such that the specialization splits for almost all . Then show that itself is split.

As a comparison, if you replace by , then although the condition that 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?

Does it not follow from Faddeev (http://www.ams.org/mathscinet-getitem?mr=47632) ?

Perhaps? I confess that it is not obvious to me that it does.