Project C7: Derived splinters and full exceptional collections

Project C7 lies at the juncture of algebraic geometry and representation theory of finite-dimensional algebras. Its goal is to study algebraic schemes defined over a field of positive characteristic (or a Dedekind ring), which are derived splinters. The purely geometric (cohomological) splinter property of a scheme is conjecturally related to the existence of full exceptional collections in the corresponding derived category of coherent sheaves, the construction of which is going to be achieved using the technique of highest weight categories and polynomial representations of linear algebraic groups over $\mathbb{Z}$.
There is at least one job opening for this project.