منابع مشابه
Slope Filtrations in Families
In [1], Berger and Colmez introduced a theory of families of étale (φ,Γ)-modules associated to families of p-adic Galois representations. Inspired by their works, we consider families of φ-modules over a reduced affinoid algebra where the base is fixed by Frobenius actions. We prove some results in this framework including the semicontinuity of variation of HN-polygons. These results will be ap...
متن کاملSlope filtrations and (φ,Γ)-modules in families
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...
متن کاملSlope Filtrations
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 de...
متن کاملSlope Filtrations Revisited
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.
متن کاملSlope filtrations for relative Frobenius
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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ژورنال
عنوان ژورنال: Journal of the Institute of Mathematics of Jussieu
سال: 2012
ISSN: 1474-7480,1475-3030
DOI: 10.1017/s1474748012000709