Galois descent and cohomology for algebraic groups.
General linear and functor cohomology over finite fields.
Generalized support varieties for finite group schemes.
Generic Newton polygons of Ekedahl-Oort strata: Oort’s conjecture
We study the moduli space of principally polarized abelian varieties in positive characteristic. In this paper we determine the Newton polygon of any generic point of each Ekedahl-Oort stratum, by proving Oort’s conjecture on intersections of Newton polygon strata and Ekedahl-Oort strata. This result tells us a combinatorial algorithm determining the optimal upper bound of the Newton polygons of principally polarized abelian varieties with a given isomorphism type of -kernel.
Geometry of infinitesimal group schemes.
Group Schemes over artinian rings and Applications
Let be a positive integer and a complete characteristic zero discrete valuation ring with maximal ideal , absolute ramification index and perfect residue field of characteristic . In this paper we classify smooth finite dimensional formal -faithful groups over , i.e. groups on which the “multiplication by ” morphism is faithfully flat, in particular -divisible groups. As applications, we prove that -divisible groups over , and the morphisms between them, lift canonically to , and...
Groupes associés aux algèbres de Kac-Moody
Groupes henséliens
Groupes libres et algebres de groupes en geometrie algebrique.
Groupes réductifs sur un corps local : II. Schémas en groupes. Existence d'une donnée radicielle valuée