In this talk we consider a normal toric algebra R over a field of characteristic p >0. The module M of p^e-th roots of R is then the direct sum of so-called conic modules. With a quite combinatorial method we construct certain complexes of conic modules over R and explain how these yield projective resolutions of simple modules over the endomorphism ring End_R(M).
Thus we obtain a bound on the global dimension of End_R(M), which shows that this endomorphism ring is a noncommutative resolution of singularities (NCR) of R (or Spec(R)). This is joint work with Greg Muller and Karen E. Smith. Speaker(s): Eleonore Faber (University of Michigan)