Slope filtrations revisited

By Kiran S. Kedlaya. Documenta Mathematica, 2005

117 citations recorded by the source corpus.

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.

Subfields: Civil and Structural Engineering, Management, Monitoring, Policy and Law, Soil Science

View Paper: https://www.semanticscholar.org/paper/fdd9bbab83bb7722e783b4f4a5b469716271a6d7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. U. Hartl
2. Kentaro Nakamura
3. Ruochuan Liu
4. Y. Andr'e
5. Laurent Berger

In Management, Monitoring, Policy and Law

1. U. Hartl
2. Kentaro Nakamura
3. Ruochuan Liu
4. Y. Andr'e
5. Laurent Berger

In Soil Science

1. U. Hartl
2. Kentaro Nakamura
3. Ruochuan Liu
4. Y. Andr'e
5. Laurent Berger

Citations in the corpus

• Relative P-adic Hodge Theory: Foundations (2013, methodology): “One is thus led naturally to consider similar constructions starting from the ring of Witt vectors over a general analytic field; the analogues of the results of [67] were worked out by the first author in [68].”
• Classification of two-dimensional split trianguline representations of p-adic fields (2008, methodology): “B † , see 1.2 of this paper.) is a B´ezout domain by [Ke05,Theorem2.9.6] (In the definition of”
• Period spaces for Hodge structures in equal characteristic (2005, methodology): “The reader should note that in case B = L the rings L〈 z ζ 〉[z −1], L((z)), and L〈 z ζ , z −1} are the equal characteristic analogues of the rings that Kedlaya [41] calls Γcon[π −1], Γ[π−1], and Γan, con, respectively, and Colmez [18] calls B L, BL, and B † rig,L, respectively.”
• Slope filtrations (2008, background): “4), the former lies ab ove the latter, with the same end-points [54].”
• Slope filtrations for relative Frobenius (2006, methodology): “(Note that [22] itself generalizes [20] in a different direction, replacing the power series rings by somewhat more general objects; we do not treat that generalization here.”
• Construction de (φ,Γ)-modules: représentations p-adiques et B-paires (2008, background): “1 de [Kedlaya 2005] qui nous permet de trouver une base de D dans laquelle p−nMat(φd) ∈ GLd(AK ).”
• Semistable reduction for overconvergent F-isocrystals, IV: local semistable reduction at nonmonomial valuations (2006, background): “1]; note that this depends on the generalized slope filtration theorem of [13], not just on the original form of the theorem of [11].”