68 research outputs found
Images directes II: F-isocristaux convergents
70 pagesThis article is the second one of a series of three articles devoted to direct images of isocrystals: here we consider convergent isocrystals with Frobenius structure. Let V be a complete discrete valuation ring, with residue field k = V/m of characteristic p > 0 and fraction field K of characteristic 0. Firstly we characterize convergent F-isocrystals on a smooth affine k-scheme. Secondly, for perfect k and after a detailed exposition of the Teichmûller liftings, especially for the affine rigid line, we derive the existence of Frobenius isomorphisms on the direct images of convergent F-isocrystals under a proper smooth and liftable k-morphism
Cohomologie syntomique: liens avec les cohomologies Ă©tale et rigide
26 pagesSyntomic cohomology here defined yields a link between rigid cohomology and etale cohomology, viewing the last one as the fixed points under Frobenius of the former one. Let V be a complete discrete valuation ring, with perfect residue field k = V/m of characteristic p > 0 and fraction field K of characteristic 0. Having defined syntomic cohomology with compact supports of an abelian sheaf G on a k-scheme X, we show that it coincides with etale cohomology with compact supports when G is a lisse sheaf. If moreover the convergent F-isocrystal associated to G comes from an overconvergent isocrystal E, then the rigid cohomology of E expresses as a limit of syntomic cohomologies: then the etale cohomology with compact supports of G is the fixed points of Frobenius acting on the rigid cohomology of E
Images directes III: F-isocristaux surconvergents
This article is the third one of a series of three articles devoted to direct
images of isocrystals: here we consider overconvergent isocrystals with
Frobenius structure. For a liftable proper smooth morphism we establish the
overconvergence of direct images, owing to the first article and the existence
of lifts of Frobenius. This result partially answers a conjecture of Berthelot
on the overconvergence of direct images of overconvergent F-isocrystals under a
proper smooth morphism.Comment: 36 page
Images directes I: Espaces rigides analytiques et images directes
57 pagesInternational audienceThis article is the first one of a series of three articles devoted to direct images of isocrystals: here we consider isocrystals without Frobenius structure; in the second one (resp. the third one ), we will introduce a Frobenius structure in the convergent (resp. overconvergent) context. For a liftable proper smooth morphism we establish the overconvergence of direct images, owing to a base change theorem for a proper morphism between rigid analytic spaces. This result partially answers a conjecture of Berthelot on the overconvergence of direct images under a proper smooth morphism
Proposal for a loophole-free violation of Bell inequalities with a set of single photons and homodyne measurements
We demonstrate that different kind of mesoscopic quantum states of light can
be efficiently generated from a simple iterative scheme using homodyne
heralding. These states exhibit strong non-classical features, and are of great
interest for many applications such as quantum error-correcting codes or
fundamental testings. On this basis we propose a protocol allowing a large
loophole-free violation of a CHSH-type Bell inequality with a remarkable
robustness to line losses
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