Serre's problem for multiple conics

We prove the refined Loughran--Smeets conjecture of Loughran--Rome--Sofos for a wide class of varieties arising as products of conic bundles. One interesting feature of our varieties is that the subordinate Brauer group may be arbitrarily large. We make significant progress towards a question of Serre on the zero loci of systems of quaternion algebras defined over $Q(t_1, \ldots, t_n)$. This is joint work with Peter Koymans and Nick Rome.