Frobenius morphisms and derived categories on two dimensional toric   Deligne-Mumford stacks
  For a toric Deligne-Mumford (DM) stack, we can consider a certain generalization of the Frobenius endomorphism. For such an endomorphism on a two-dimensional toric DM stack, we show that the push-forward of the structure sheaf generates the bounded derived category of coherent sheaves on the toric DM stack.   We also choose a full strong exceptional collection from the set of direct summands of the push-forward in several examples of two dimensional toric DM orbifolds. 
Ryo Ohkawa, Hokuto Uehara
math.AG