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THE HITCHIN CONNECTION IN ARBITRARY CHARACTERISTIC

Published online by Cambridge University Press:  11 May 2022

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, 34095Montpellier Cedex 5, France
Thomas Baier
Affiliation:
CAMGSD, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001Lisboa, Portugal (tbaier@math.tecnico.ulisboa.pt)

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.

Type
Research Article
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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