Graded-Injective Modules and Bass Numbers of Veronese Submodules

Let R be a standard graded, finitely generated algebra over a field, and let M be a graded module over R with all Bass numbers finite. Set (-)⁽ⁿ⁾ to be the n-th Veronese functor. We compute the Bass numbers of M⁽ⁿ⁾ over the ring R⁽ⁿ⁾ for all prime ideals of R⁽ⁿ⁾ that are not the homogeneous maximal ideal in terms of the Bass numbers of M over R. As an application to local cohomology modules, we determine the Bass numbers of H_I∩ R⁽ⁿ⁾ⁱ(R⁽ⁿ⁾) over the ring R⁽ⁿ⁾ in the case where HIⁱ(R) has finite Bass numbers over R and I is a graded ideal.