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    Kedlaya, Kiran S. 2015. Local and global structure of connections on nonarchimedean curves. Compositio Mathematica, Vol. 151, Issue. 06, p. 1096.

    Xiao, Liang 2012. On ramification filtrations and p-adic differential equations, II: mixed characteristic case. Compositio Mathematica, Vol. 148, Issue. 02, p. 415.

    Xiao, Liang 2012. On the refined ramification filtrations in the equal characteristic case. Algebra & Number Theory, Vol. 6, Issue. 8, p. 1579.

    Kedlaya, Kiran S. 2011. Swan conductors for p-adic differential modules. II Global variation. Journal of the Institute of Mathematics of Jussieu, Vol. 10, Issue. 01, p. 191.

    Shiho, Atsushi 2010. Cut-by-curves criterion for the overconvergence of p-adic differential equations. manuscripta mathematica, Vol. 132, Issue. 3-4, p. 517.

  • Journal of the Institute of Mathematics of Jussieu, Volume 9, Issue 1
  • January 2010, pp. 155-201

Differential modules on p-adic polyannuli

  • Kiran S. Kedlaya (a1) and Liang Xiao (a2)
  • DOI:
  • Published online: 01 May 2009

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.

5.D. Eisenbud , Commutative algebra, Graduate Texts in Mathematics, Volume 150 (Springer, 1995).

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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.

14.K. S. Kedlaya and P. Tynan , Detecting integral polyhedral functions, Confluentes Math. 1 (2009), 123.

16.O. Ore , Theory of non-commutative polynomials, Annals Math. 34 (1933), 480508.

17.P. Ribenboim , The theory of classical valuations (Springer, 1999).

19.P. Schneider , Nonarchimedean functional analysis (Springer, 2002).

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
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