The conjecture that simple fields are pseudo-algebraically closed

A field $K$ is simple if its theory is simple, and it is pseudo-algebraically closed if every geometrically irreducible $K$-variety has a $K$-rational point.

Simple-field conjecture. Every simple field is pseudo-algebraically closed.

This is one of the two well-known conjectures relating model-theoretic properties of fields to algebraic properties; the source gives no resolution status.