Abstract: In a recent paper Trevor Hyde discovered, and proved by direct calculation, a relationship between the probabilities of different factorization types of degree n polynomials over finite fields, and the decomposition of the cohomology of the configuration space of n points in R^3 as a representation of S_n. The “shape” of the formula is reminiscent of the Grothendieck-Lefschetz trace formula, and Hyde asked whether there was such a geometric interpretation of the result. It’s far from clear how such an interpretation should look, given that the configuration space of points in R^3 is definitely not a complex algebraic variety! We answer the question by constructing a curious and highly nonseparated algebraic space with some interesting geometry; its complex analytification has the homotopy type of the configuration space of points in R^3, and the Grothendieck-Lefschetz trace formula applied to the algebraic space produces (a new proof of) Hyde’s theorem. The construction generalizes to prove an analogue of Hyde’s theorem for an arbitrary Weyl group. (Joint w. Phil Tosteson)