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The local index and the Swan conductor

Published online by Cambridge University Press:  04 December 2007

TSUZUKI NOBUO
TSUZUKI NOBUO
Affiliation:
Department of Mathematics, Faculty of Science, Hiroshima University, Higashi-Hiroshima, 739, Japan; e-mail: tsuzuki@math.sci.hiroshima-u.ac.jp
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Abstract

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In this paper we study local indices of systems of p-adic linearly differential equations which arise from p-adic representations of the absolute Galois group of local field of characteristic p with finite monodromy. We show the induction formula of the local index of p-adic differential equations and prove the equality between the local index of differential equations and the Swan conductor of p-adic Galois representations by inductive methods.

Keywords

etale φ-∇-moduleslocal indexSwan conductor.
Type
Research Article
Information
Compositio Mathematica , Volume 111 , Issue 3 , May 1998 , pp. 245 - 288
Copyright
© 1998 Kluwer Academic Publishers