Notes on the Cauchy–Kowalevski Theorem for E-modules

For a coherent EX-module M, Kashiwara and Schapira introduced the complex RHomEX(M, OX) of holomorphic solutions to M. Very recently this complex was used by R. Ishimura (1998, J. Math. Pures Appl.77, 647–654) to formulate and establish the Cauchy–Kowalevski theorem for E-modules. In this paper, we will give a rigorous proof of some arguments of Ishimura.