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Invariants, torsion indices and oriented cohomology of complete flags

Baptiste Calmès, Viktor Petrov, Kirill Zainoulline (2013)

Annales scientifiques de l'École Normale Supérieure

Let  G be a split semisimple linear algebraic group over a field and let  T be a split maximal torus of  G . Let  𝗁 be an oriented cohomology (algebraic cobordism, connective K -theory, Chow groups, Grothendieck’s K 0 , etc.) with formal group law F . We construct a ring from F and the characters of  T , that we call a formal group ring, and we define a characteristic ring morphism c from this formal group ring to  𝗁 ( G / B ) where G / B is the variety of Borel subgroups of  G . Our main result says that when the torsion index...

Is the Luna stratification intrinsic?

Jochen Kuttler, Zinovy Reichstein (2008)

Annales de l’institut Fourier

Let G → GL ( V ) be a representation of a reductive linear algebraic group G on a finite-dimensional vector space V , defined over an algebraically closed field of characteristic zero. The categorical quotient X = V // G carries a natural stratification, due to D. Luna. This paper addresses the following questions:(i) Is the Luna stratification of X intrinsic? That is, does every automorphism of V // G map each stratum to another stratum?(ii) Are the individual Luna strata in X intrinsic? That is, does every automorphism...

Jordan pairs of quadratic forms with values in invertible modules.

Hisatoshi Ikai (2007)

Collectanea Mathematica

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

Rolf Farnsteiner (2014)

Journal of the European Mathematical Society

In this article we study the interplay between algebro-geometric notions related to π -points and structural features of the stable Auslander-Reiten quiver of a finite group scheme. We show that π -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 π -points on the other. Special attention is given to components containing Carlson modules, constantly supported modules, and endo-trivial modules.

La filtration canonique des points de torsion des groupes p -divisibles

Laurent Fargues (2011)

Annales scientifiques de l'École Normale Supérieure

Étant donnés un entier n ≥ 1 et un groupe de Barsotti-Tate tronqué d’échelon  n et de dimension d sur un anneau de valuation d’inégales caractéristiques, nous donnons une borne explicite sur son invariant de Hasse qui implique que sa filtration de Harder-Narasimhan possède un sous-groupe libre de rang d . Lorsque n = 1 nous redémontrons également le théorème d’Abbes-Mokrane ([120]) et de Tian ([164]) par des méthodes locales. On applique cela aux familles p -adiques de tels objets et en particulier à certaines...

Le système d’Euler de Kato

Shanwen Wang (2013)

Journal de Théorie des Nombres de Bordeaux

Ce texte est consacré au système d’Euler de Kato, construit à partir des unités modulaires, et à son image par l’application exponentielle duale (loi de réciprocité explicite de Kato). La présentation que nous en donnons est sensiblement différente de la présentation originelle de Kato.

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