Abstract:

A hypergeometric local system on P \ { 0,1,\infty}, irreducible and defined over $\mathbb{Q}$, is known to be motivic, but which geometry it comes from is a separate question. 
I will describe an explicit family of affine varieties in an algebraic torus and explain that the local system is the top graded piece of the weight filtration on the primitive middle compactly supported cohomology of the family. 
The result is unconditional for families of curves and of even-dimensional varieties.