Slope Filtrations
نویسنده
چکیده
Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-adic theories, geometry of numbers... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of common properties. We propose a unified abstract treatment of slope filtrations, and survey how new ties between different domains have been woven by dint of deep correspondences between different concrete slope filtrations.
منابع مشابه
Arithmetic Fujita approximation
— We prove an arithmetic analogue of Fujita’s approximation theorem in Arakelov geometry, conjectured by Moriwaki, by using slope method and measures associated to R-filtrations. Résumé. — On démontre un analogue arithmétique du théorème d’approximation de Fujita en géométrie d’Arakelov — conjecturé par Moriwaki — par la méthode de pentes et les mesures associées aux R-filtrations.
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We give a “second generation” exposition of the slope filtration theorem for modules with Frobenius action over the Robba ring, providing a number of simplifications in the arguments. Some of these are inspired by parallel work of Hartl and Pink, which points out some analogies with the formalism of stable vector bundles.
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These are the notes for a three-lecture minicourse given at the Institut Henri Poincaré in January 2010 as part of the Galois Trimester. The first lecture reviews the theory of slopes and slope filtrations for Frobenius actions (φ-modules) over the Robba ring, the link to p-adic Hodge theory via the work of Berger, and the analogue of Dieudonné-Manin classifications over the Robba ring. The sec...
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Comparison between multidimensional persistent Betti numbers is often based on the multidimensional matching distance. While this metric is rather simple to define and compute by considering a suitable family of filtering functions associated with lines having a positive slope, it has two main drawbacks. First, it forgets the natural link between the homological properties of filtrations associ...
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The slope filtration theorem gives a partial analogue of the eigenspace decomposition of a linear transformation, for a Frobenius-semilinear endomorphism of a finite free module over the Robba ring (the ring of germs of rigid analytic functions on an unspecified open annulus of outer radius 1) over a discretely valued field. In this paper, we give a third-generation proof of this theorem, which...
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