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arXiv · 2002.12288

The Hitchin connection in arbitrary characteristic

Thomas Baier·Michele Bolognesi·Johan Martens·Christian Pauly
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Abstract

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.

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Thomas Baier, Michele Bolognesi, Johan Martens, Christian Pauly. 2020-02-27. The Hitchin connection in arbitrary characteristic. https://doi.org/10.1017/s1474748022000196

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