Musings on microlocal analysis in characteristic p
نویسنده
چکیده
This sketch is intended as a summary of my thoughts during the fall of 2005, attempting to understand a conversation with Kontsevich that summer as well as a little bit of his preprint [1]. The theme is to explore further the geometric meaning of the p-curvature, which can provide an analogy to the characteristic variety in microlocal analysis. Let S be a scheme and let X/S be a smooth S-scheme. We shall be interested in integrable systems of linear partial differential equations on X/S. These can be described in several ways. Let ΩX/S be the sheaf of Kahler differentials on X/S and let TX/S be its dual, which can be identified with the sheaf of derivation OX → OX relative to S. Recall that a connection on a sheaf E of OX-modules is an OS-linear map
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