We consider variational properties of some numerical invariants, measuring convergence of local horizontal sections, associated to differential modules on polyannuli over a nonarchimedean field of characteristic 0. This extends prior work in the one-dimensional case of Christol, Dwork, Robba, Young, et al. Our results do not require positive residue characteristic; thus besides their relevance to the study of Swan conductors for isocrystals, they are germane to the formal classification of flat meromorphic connections on complex manifolds.
(Received May 19 2008)
(Accepted July 22 2008)
Keywordsdifferential modules; polyannuli; nonarchimedean field; generic radius of convergence
AMS 2000 Mathematics subject classificationPrimary 14G22