Singularities in Positive-Characteristic Algebraic Geometry

SIPOCAG aims to understand and classify singularities occurring in positive-characteristic from two points of view: First, to understand the indecomposable summands arising via the Frobenius morphism of a ring or a variety, and second, to understand the relation between the theory of arc/jet schemes and the ""standard"" singularities of positive-characteristic commutative algebra. Towards the first objective, given a ring R in characteristic p, one obtains a new module by restricting scalars along the Frobenius self-map on R. The properties of resulting module reflect the singularities of R