Macarena Peche Irissarry: Reduction of G-ordinary crystalline representations with G-structure

Fontaine’s functor allows us to associate an isocrystal to any crystalline representation. For a reductive group , we study the reduction of lattices inside a germ of crystalline representations with -structure to lattices (which are crystals) with -structure inside . Using Kisin modules theory, we give a description of this reduction in terms of , in the case where the representation is ( -)ordinary. In order to do that, first we need to generalize Fargues’ construction of the Harder-Narasimhan filtration for -divisible groups to Kisin modules.