Modules of constant Jordan type, pullbacks of bundles and generic kernel filtrations

摘要

Let kE denote the group algebra of an elementary abelian p-group of rank r over an algebraically closed field of characteristic p. We investigate the functors F-i from kE-modules of constant Jordan type to vector bundles on Pr-1(k), constructed by Benson and Pevtsova. For a kE-module M of constant Jordan type, we show that restricting the sheaf F-i(M) to a dimension s - 1 linear subvariety of Pr-1(k) is equivalent to restricting M along a corresponding rank s shifted subgroup of kE and then applying F-i.