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The Hitchin connection in arbitrary characteristic

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Thomas Baier
  • Fonction : Auteur
Johan Martens
  • Fonction : Auteur
Christian Pauly
  • Fonction : Auteur


We give an algebro-geometric construction of the Hitchin connection, valid also in positive characteristic (with a few exceptions). A key ingredient is a substitute for the Narasimhan-Atiyah-Bott K\"ahler form that realizes the Chern class of the determinant-of-cohomology line bundle on the moduli space of bundles on a curve. As replacement we use an explicit realisation of the Atiyah class of this line bundle, based on the theory of the trace complex due to Beilinson-Schechtman and Bloch-Esnault.

Dates et versions

hal-03413177 , version 1 (03-11-2021)



Michele Bolognesi, Thomas Baier, Johan Martens, Christian Pauly. The Hitchin connection in arbitrary characteristic. 2021. ⟨hal-03413177⟩
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