We examine the projective dimensions of Mackey functors and cohomological Mackey functors. We show over a field of characteristic p that cohomological Mackey functors are Gorenstein if and only if Sylow p-subgroups are cyclic or dihedral, and they have finite global dimension if and only if the group order is invertible or Sylow subgroups are cyclic of order 2. By contrast, we show that the onl...

Let Q be a finite connected quiver and Λ the radical square zero algebra of Q. We give bijection between reduced differential projective modules over representations opposite If has oriented cycles is not basic cycle, we prove that dual numbers virtually Gorenstein.

For projective varieties with a certain class of ‘mild’ isolated singularities and for projective threefolds with arbitrary Gorenstein canonical singularities, we show that the stringy Hodge numbers satisfy the Hard Lefschetz property (i.e. h st ≤ h p+1,q+1 st for p+ q ≤ d− 2, where d is the dimension of the variety). This result fits nicely with a 6-dimensional counterexample of Mustaţă and Pa...

We present and study the concept of m-periodic Gorenstein objects relative to a pair (A,B) classes in an abelian category, as generalization m-strongly projective modules over associative rings. prove several properties when satisfies certain homological conditions, like for instance is GP-admissible pair. Connections dimensions these pairs are also established.