Abstract:  For a local $F$-finite ring, the splitting prime is an ``obstruction'' to strong $F$-regularity. In this talk, we will define the self-map on the Frobenius split locus of a ring $R$ which sends a point $P$ to the splitting prime of $R_P$, and discuss the generalization of this map to the setting of Cartier algebras. We will go over some properties of this map and, as an application, will show how it behaves for Stanley-Reisner rings.

For anyone interested in attending the talk, please reach out to Janet Vassilev by email to get the link for the Team.