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Katz Correspondence for Quasi-Unipotent Overconvergent Isocrystals

Published online by Cambridge University Press:  04 December 2007

Shigeki Matsuda
Affiliation:
Department of Mathematics and Informatics, Chiba University, Japan. matsu@math.s.chiba-u.ac.jp
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Abstract

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Let k be a field and X = Spec (k[t,t−1]). Katz proved that a differential equations with coefficients in k((t−1)) is uniquely extended to a special algebraic differential equation on X when k is of characteristic 0. He also proved that a finite extension of k((t−1)) is uniquely extended to a special covering of X when k is of any characteristic. These theorems are called canonical extension or Katz correspondence. We shall prove a p-adic analogue of canonical extension for quasi-unipotent overconvergent isocrystals. As a consequence, we can show that the local index of a quasi-unipotent overconvergent is equal to its Swan conductor.

Type
Research Article
Copyright
© 2002 Kluwer Academic Publishers