Semistable reduction for overconvergent F-isocrystals, III: Local semistable reduction at monomial valuations

Abstract

We resolve the local semistable reduction problem for overconvergent F-isocrystals at monomial valuations (Abhyankar valuations of height 1 and residue transcendence degree 0). We first introduce a higher-dimensional analogue of the generic radius of convergence for a p-adic differential module, which obeys a convexity property. We then combine this convexity property with a form of the p-adic local monodromy theorem for so-called fake annuli.

36 pages; v3: refereed version; adds appendix with two examples

References in corpus (5)

• Slope filtrations revisited
• Slope filtrations for relative Frobenius
• Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuations
• Overholonomicity of overconvergent $F$-isocrystals over smooth varieties
• The p-adic local monodromy theorem for fake annuli

Cited by in corpus (24)

• Relative log convergent cohomology and relative rigid cohomology I
• The eigencurve over the boundary of weight space
• Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuations
• Dynamics on Berkovich spaces in low dimensions
• Theory of weights in p-adic cohomology
• Langlands correspondence for isocrystals and the existence of crystalline companions for curves
• Local and global structure of connections on nonarchimedean curves
• Bessel $F$-isocrystals for reductive groups
• Parabolicity conjecture of $F$-isocrystals
• Etale and crystalline companions, I
• A Lefschetz theorem for overconvergent isocrystals with Frobenius structure
• On Beilinson's equivalence for $p$-adic cohomology
• Unipotent monodromy and arithmetic D-modules
• On refined ramification filtrations in the equal characteristic case
• Logarithmic $p$-bases and arithmetical differential modules
• A note on logarithmic growth of solutions of $p$-adic differential equations without solvability
• Logarithmic growth filtrations for $(\phi ,\nabla )$-modules over the bounded Robba ring
• Betti number estimates in p-adic cohomology
• Detecting integral polyhedral functions
• Around the nearby cycle functor for arithmetic $\mathcal{D}$-modules
• Analytic Geometry and Hodge-Frobenius Structure
• On extension of overconvergent log isocrystals on log smooth varieties
• Tamagawa number formula with coefficients over varieties in positive characteristic
• On logarithmic extension of overconvergent isocrystals