Slope filtrations for relative Frobenius

Abstract

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.

40 pages; v2: refereed version, minor changes

References in corpus (2)

• Slope filtrations revisited
• Full faithfulness for overconvergent F-isocrystals

Cited by in corpus (13)

• Semistable reduction for overconvergent F-isocrystals, III: Local semistable reduction at monomial valuations
• Classification of two dimensional split trianguline representations of $p$-adic fields
• Deformations of trianguline B-pairs and Zariski density of two dimensional crystalline representations
• Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuations
• Locally analytic vectors of unitary principal series of GL_2(Qp)
• The universal family of semi-stable p-adic Galois representations
• Frobenius modules over multivariate Robba rings
• Classification of subbundles on the Fargues-Fontaine curve
• Triangulordinary Selmer Groups
• On Families of (Phi,Gamma)-modules
• Categorification of Harder-Narasimhan Theory via slope functions
• Cohomology of $(\phi ,\tau )$-modules
• A group-theoretic generalization of the $p$-adic local monodromy theorem