A ug 2 00 5 The p - adic local monodromy theorem for fake annuli , I : The monomial case

The p-adic local monodromy theorem for fake annuli

We establish a generalization of the p-adic local monodromy theorem (of André, Mebkhout, and the author) in which differential equations on rigid analytic annuli are replaced by differential equations on so-called “fake annuli”. The latter correspond loosely to completions of a Laurent polynomial ring with respect to a monomial valuation. The result represents a step towards a higher-dimensiona...

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

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...

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

We resolve the local semistable reduction problem for overconvergent F -isocrystals at monomial valuations (Abhyankar valuations of height 1 and residue transcendence degree zero). 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-a...

A ug 2 00 1 Derivatives of p - adic L - functions , Heegner cycles and monodromy modules attached to modular forms

2 00 6 Swan conductors for p - adic differential modules , I : A local construction

We define a numerical invariant, the differential Swan conductor, for certain differential modules on a rigid analytic annulus over a p-adic field. This gives a definition of a conductor for p-adic Galois representations with finite local monodromy over an equal characteristic discretely valued field, which agrees with the usual Swan conductor when the residue field is perfect. We also establis...