An index theorem for 𝑝-adic differential operators

Adolphson, A.

doi:10.1090/S0002-9947-1976-0387284-4

An index theorem for $p$-adic differential operators
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Trans. Amer. Math. Soc. 216 (1976), 279-293 Request permission

Abstract:

A system of first order linear differential operators satisfying conditions arising naturally in geometry (rational function coefficients, regular singularities, non-Liouville exponents) is considered. It is shown that the index of the system on certain spaces of holomorphic functions can be calculated by restricting to a subspace of rational functions. This is applied to obtain an explicit formula for the index of a single kth order linear differential operator.

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Fonctions analytiques sur les corps values ultra-métriques complets