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THE HITCHIN CONNECTION IN ARBITRARY CHARACTERISTIC

Published online by Cambridge University Press:  11 May 2022

Christian Pauly ,
Johan Martens ,
Michele Bolognesi Open the ORCID record for Michele Bolognesi [Opens in a new window]  and
Thomas Baier
Christian Pauly
Affiliation:
Laboratoire de Mathématiques J.A. Dieudonné, UMR 7351 CNRS, Université de Nice Sophia-Antipolis, 06108 Nice Cedex 02, France (pauly@unice.fr)
Johan Martens
Affiliation:
School of Mathematics and Maxwell Institute, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom (johan.martens@ed.ac.uk)
Michele Bolognesi
Affiliation:
Institut Montpelliérain Alexander Grothendieck, UMR 5149 CNRS, Université de Montpellier, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France (michele.bolognesi@umontpellier.fr)
Thomas Baier
Affiliation:
CAMGSD, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal (tbaier@math.tecnico.ulisboa.pt)
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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 Kähler 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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Type
Research Article
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Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 1 , January 2023 , pp. 449 - 492
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© The Author(s), 2022. Published by Cambridge University Press

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