Generalized Support Varieties for Finite Group Schemes

  • Julia Pevtsova


We construct two families of refinements of the (projectivized) support variety of a finite dimensional module for a finite group scheme . For an arbitrary finite group scheme, we associate a family of non-maximal rank varieties , , to a -module . For infinitesimal, we construct a finer family of locally closed subvarieties of the variety of one parameter subgroups of for any partition of . For an arbitrary finite group scheme , a -module of constant rank, and a cohomology class in we introduce the zero locus . We show that is a closed subvariety, and relate it to the non-maximal rank varieties. We also extend the construction of to an arbitrary extension class whenever and are -modules of constant Jordan type.