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Higgs cohomology, p-curvature, and the Cartier isomorphism
Published online by Cambridge University Press: 04 December 2007
Abstract
Let X/S be a smooth morphism of schemes in characteristic p and let $(E,\nabla)$ be a sheaf of $\mathcal{O}_{X}$-modules with integrable connection on X. We give a formula for the cohomology sheaves of the de Rham complex of $(E,\nabla)$ in terms of a Higgs complex constructed from the p-curvature of $(E,\nabla)$. This formula generalizes the classical Cartier isomorphism, with which it agrees when $(E,\nabla)$ is the constant connection.
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- Research Article
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- Foundation Compositio Mathematica 2004
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