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Differential modules on p-adic polyannuli

  • Kiran S. Kedlaya (a1) and Liang Xiao (a2)

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.

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3. G. Christol and B. Dwork , Modules différentielles sur les couronnes, Annales Inst. Fourier 44 (1994), 663701.

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8. K. S. Kedlaya , Swan conductors for p-adic differential modules, I, A local construction, Alg. Num. Theory 1 (2007), 269300.

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20. P. T. Young , Radii of convergence and index for p-adic differential operators, Trans. Am. Math. Soc. 333 (1992), 769785.

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Journal of the Institute of Mathematics of Jussieu
  • ISSN: 1474-7480
  • EISSN: 1475-3030
  • URL: /core/journals/journal-of-the-institute-of-mathematics-of-jussieu
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