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Documents  14F10 | enregistrements trouvés : 2

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We will show that there exists a correspondence between smooth $l$-adic sheaves and overconvergent $F$-isocrystals over a curve preserving the Frobenius eigenvalues. Moreover, we show the existence of $l$-adic companions associated to overconvergent $F$-isocrystals for smooth varieties.
Some part of the work is done jointly with Esnault.

12H25 ; 14F30 ; 14F10

In the local classification of differential equations of one complex variable, torsors under a certain sheaf of algebraic groups (the Stokes sheaf) play a central role. On the other hand, Deligne defined in positive characteristic a notion of skeletons for l-adic local systems on a smooth variety, constructed an algebraic variety parametrizing skeletons and raised the question wether every skeleton comes from an actual l-adic local system. We will explain how to use a variant of Deligne's skeleton conjecture in characteristic 0 to prove the existence of an algebraic variety parametrizing Stokes torsors. We will show how the geometry of this moduli can be used to prove new finiteness results on differential equations. In the local classification of differential equations of one complex variable, torsors under a certain sheaf of algebraic groups (the Stokes sheaf) play a central role. On the other hand, Deligne defined in positive characteristic a notion of skeletons for l-adic local systems on a smooth variety, constructed an algebraic variety parametrizing skeletons and raised the question wether every skeleton comes from an actual l-adic local system. We ...

32C38 ; 14F10

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