The F-signature is a numerical invariant of singularities which measures the asymptotic number of splittings of iterates of Frobenius. In this talk, I will discuss a generalization of the F-signature along an arbitrary cofinite ideal -- analagous to the situation for Hilbert-Kunz multiplicity. In particular, this generalization allows for a transformation rule for F-signature under an arbitrary finite morphism. This is joint work in progress with Javier Carvajal-Rojas and Karl Schwede. Speaker(s): Kevin Tucker (University of Illinois at Chicago)