2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210591We 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 zero. 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.47 pages; v4: Lemma 2.2.3 correctedNumber TheoryAlgebraic Geometry14G22text