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
Height one Hopf algebras in low ramification.
Homological Properties of Certain Arithmetic Groups in the Function Field Case.
Infinitesimal unipotent group schemes of complexity 1
We classify the uniserial infinitesimal unipotent commutative groups of finite representation type over algebraically closed fields. As an application we provide detailed information on the structure of those infinitesimal groups whose distribution algebras have a representation-finite principal block.
Invariante Zwischenkörper endlicher Körpererweiterungen.
Invariants de classes : propriétés fonctorielles et applications à l’étude du noyau
L’homomorphisme de classes mesure la structure galoisienne de torseurs – sous un schéma en groupes fini et plat – obtenus grâce au cobord d’une suite exacte. Son introduction est due à Martin Taylor (la suite exacte étant une isogénie entre schémas abéliens). Nous commençons par énoncer quelques propriétés générales de cet homomorphisme, puis nous poursuivons son étude dans le cas où la suite exacte est donnée par la multiplication par sur une extension d’un schéma abélien par un tore.
Isomorphic Chevalley groups over integral domains
Jacobienne locale d'une courbe formelle relative
Jordan pairs of quadratic forms with values in invertible modules.
Jordan pairs of quadratic forms are generalized so that they have forms with values in invertible modules. The role of such pairs turns out to be natural in describing 'big cells', a kind of open charts around unit sections, of Clifford and orthogonal groups as group schemes. Group germ structures on big cells are particularly interested in and related also to Cayley-Lipschitz transforms.
Jordan types for indecomposable modules of finite group schemes
In this article we study the interplay between algebro-geometric notions related to -points and structural features of the stable Auslander-Reiten quiver of a finite group scheme. We show that -points give rise to a number of new invariants of the AR-quiver on one hand, and exploit combinatorial properties of AR-components to obtain information on -points on the other. Special attention is given to components containing Carlson modules, constantly supported modules, and endo-trivial modules.
Konstruktion der Integrale von endlichen algebraischen Gruppen.