N ov 2 00 6 Swan conductors for p - adic differential modules , I : A local construction Kiran
نویسنده
چکیده
We define a numerical invariant, the differential Swan conductor, for certain differential modules on a rigid analytic annulus over a p-adic field. This gives a definition of a conductor for p-adic Galois representations with finite local monodromy over an equal characteristic discretely valued field, which agrees with the usual Swan conductor when the residue field is perfect.
منابع مشابه
2 00 6 Swan conductors for p - adic differential modules , I : A local construction
We define a numerical invariant, the differential Swan conductor, for certain differential modules on a rigid analytic annulus over a p-adic field. This gives a definition of a conductor for p-adic Galois representations with finite local monodromy over an equal characteristic discretely valued field, which agrees with the usual Swan conductor when the residue field is perfect. We also establis...
متن کاملSwan conductors for p-adic differential modules, I: A local construction
We define a numerical invariant, the differential Swan conductor, for certain differential modules on a rigid analytic annulus over a p-adic field. This gives a definition of a conductor for p-adic Galois representations with finite local monodromy over an equal characteristic discretely valued field, which agrees with the usual Swan conductor when the residue field is perfect. We also establis...
متن کامل1 M ay 2 00 7 Swan conductors for p - adic differential modules , II : Global variation
Using a local construction from a previous paper, we exhibit a numerical invariant, the differential Swan conductor, for an overconvergent isocrystal on a variety over a perfect field of positive characteristic along a boundary divisor; this leads to an analogous construction for certain p-adic representations of the étale fundamental group of a variety. We then demonstrate some variational pro...
متن کاملSwan conductors for p-adic differential modules, II: Global variation
Using a local construction from a previous paper, we exhibit a numerical invariant, the differential Swan conductor, for an isocrystal on a variety over a perfect field of positive characteristic overconvergent along a boundary divisor; this leads to an analogous construction for certain p-adic and l-adic representations of the étale fundamental group of a variety. We then demonstrate some vari...
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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 zero. This extends prior work in the onedimensional case of Christol, Dwork, Robba, Young, et al. Our results do not require positive residue characteristic; thus besides their relevanc...
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