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Transversal crystals of finite level

Bernard Le Stum, Adolfo Quirós (1997)

Annales de l'institut Fourier

We extend Ogus’notion of T -crystal and F -span to the context of Berthelot’s crystals of level m and we study the generalization of Ogus’theorem on the equivalence between T -crystals and F -spans of width less than p .

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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