Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 2
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Chen, Tsao-Hsien and Zhu, Xinwen 2015. Non-abelian Hodge theory for algebraic curves in characteristic p. Geometric and Functional Analysis, Vol. 25, Issue. 6, p. 1706.


    Ogus, A. and Vologodsky, V. 2007. Nonabelian Hodge theory in characteristic p. Publications mathématiques de l'IHÉS, Vol. 106, Issue. 1, p. 1.


    ×

Higgs cohomology, p-curvature, and the Cartier isomorphism

  • Arthur Ogus (a1)
  • DOI: http://dx.doi.org/10.1112/S0010437X03000058
  • Published online: 01 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.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Higgs cohomology, p-curvature, and the Cartier isomorphism
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Higgs cohomology, p-curvature, and the Cartier isomorphism
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Higgs cohomology, p-curvature, and the Cartier isomorphism
      Available formats
      ×
Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: