The p-adic local monodromy theorem for fake annuli

Details The p-adic local monodromy theorem for fake annuli The p-adic local monodromy theorem for fake annuli

2005-07-24

arxiv.org/abs/math/0507496v4

Mathematics

Number Theory

38 pages; v4: refereed version, some typos fixed

Scientific paper

We establish a generalization of the p-adic local monodromy theorem (of Andre, 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-dimensional version of the p-adic local monodromy theorem (the "problem of semistable reduction"); it can also be viewed as a slightly novel presentation of the original p-adic local monodromy theorem.

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