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Invariante Divisoren und Schnitthomologie von torischen Varietäten

Gottfried Barthel, Jean-Paul Brasselet, Karl-Heinz Fieseler, Ludger Kaup (1996)

Banach Center Publications

In this article, we complete the interpretation of groups of classes of invariant divisors on a complex toric variety X of dimension n in terms of suitable (co-) homology groups. In [BBFK], we proved the following result (see Satz 1 below): Let C l D i v C ( X ) and C l D i v W ( X ) denote the groups of classes of invariant Cartier resp. Weil divisors on X. If X is non degenerate (i.e., not equivariantly isomorphic to the product of a toric variety and a torus of positive dimension), then the natural homomorphisms C l D i v C ( X ) → H 2 ( X ) and C l D i v W ( X ) → H 2 n - 2 c l d ( X ) are...

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...

J -invariant of linear algebraic groups

Viktor Petrov, Nikita Semenov, Kirill Zainoulline (2008)

Annales scientifiques de l'École Normale Supérieure

Let G be a semisimple linear algebraic group of inner type over a field F , and let X be a projective homogeneous G -variety such that G splits over the function field of X . We introduce the J -invariant of G which characterizes the motivic behavior of X , and generalizes the J -invariant defined by A. Vishik in the context of quadratic forms. We use this J -invariant to provide motivic decompositions of all generically split projective homogeneous G -varieties, e.g. Severi-Brauer varieties, Pfister quadrics,...

Killing divisor classes by algebraisation

Alexandru Buium (1985)

Annales de l'institut Fourier

It is proved that any isolated singularity of complete intersection has an algebraisation whose divisor class group is finitely generated.

Koszul duality and semisimplicity of Frobenius

Pramod N. Achar, Simon Riche (2013)

Annales de l’institut Fourier

A fundamental result of Beĭlinson–Ginzburg–Soergel states that on flag varieties and related spaces, a certain modified version of the category of ℓ -adic perverse sheaves exhibits a phenomenon known as Koszul duality. The modification essentially consists of discarding objects whose stalks carry a nonsemisimple action of Frobenius. In this paper, we prove that a number of common sheaf functors (various pull-backs and push-forwards) induce corresponding functors on the modified category or its triangulated...

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