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Travaux de Zink

William Messing (2005/2006)

Séminaire Bourbaki

The diverse Dieudonné theories have as their common goal the classification of formal groups and p -divisible groups. The most recent theory is Zink’s theory of displays. A display over a ring R is a finitely generated projective module over the ring of Witt vectors, W ( R ) , equipped with additional structures. Zink has shown that using this notion, more concrete than those previously defined, one can obtain a good theory and prove an equivalence theorem in great generality. I will give an overview of...

Twisted action of the symmetric group on the cohomology of a flag manifold

Alain Lascoux, Bernard Leclerc, Jean-Yves Thibon (1996)

Banach Center Publications

Classes dual to Schubert cycles constitute a basis on the cohomology ring of the flag manifold F, self-adjoint up to indexation with respect to the intersection form. Here, we study the bilinear form (X,Y) :=〈X·Y, c(F)〉 where X,Y are cocycles, c(F) is the total Chern class of F and〈,〉 is the intersection form. This form is related to a twisted action of the symmetric group of the cohomology ring, and to the degenerate affine Hecke algebra. We give a distinguished basis for this form, which is a...

Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations

Andreas Höring (2014)

Annales de l’institut Fourier

Let X be a normal projective variety, and let A be an ample Cartier divisor on X . Suppose that X is not the projective space. We prove that the twisted cotangent sheaf Ω X A is generically nef with respect to the polarisation  A . As an application we prove a Kobayashi-Ochiai theorem for foliations: if T X is a foliation such that det i A , then i is at most the rank of .

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