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1 results

  • Higgs cohomology, p-curvature, and the Cartier isomorphism

  • Arthur Ogus
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 1 / January 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 145-164
    Print publication:
    January 2004
    • Article
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  • 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.