On Injective Modules for Infinitesimal Algebraic Groups, I
نویسندگان
چکیده
Let G be a connected, semisimple algebraic group defined over an algebraically closed field k of characteristic p > 0. We assume that G is defined and split over the prime field k0. In general, for any positive integer r, and any affine fc-group scheme H defined over k0, the r-th infinitesimal subgroup scheme Hr of H is defined to be the (scheme-theoretic) kernel of the r-th power of the Frobenius morphism o\H-> H. In this paper we study injective modules for Gr and various other important subgroup schemes of G. Fix a maximal torus T of G defined and split over k0, and let H be any connected (reduced) T-stable closed subgroup of G. Form the subgroup scheme THr, the pullback of T under a on TH:
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