2006/09/10 by Kiran S. Kedlaya, Kedlaya, Kiran S. · 2 citations
Computer Science · Mathematics · #14F30 #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT #msc:14F30
paper · pdf · doi:10.48550/arxiv.math/0609272
40 pages; v2: refereed version, minor changes
openalex publication_date 2006/09/10 · arxiv created 2007/09/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 both introduces some new simplifications (particularly the use of faithfully flat descent, to recover the theorem from a classification theorem of Dieudonne-Manin type) and extends the result to allow an arbitrary action on coefficients (previously the action on coefficients had to itself be a lift of an absolute Frobenius). This extension is relevant to a study of (phi, Gamma)-modules associated to families of p-adic Galois representations, presently being initiated by Berger and Colmez.