The Hitchin connection in arbitrary characteristic
Algebraic Geometry
2023-03-24 v3
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.
Cite
@article{arxiv.2002.12288,
title = {The Hitchin connection in arbitrary characteristic},
author = {Thomas Baier and Michele Bolognesi and Johan Martens and Christian Pauly},
journal= {arXiv preprint arXiv:2002.12288},
year = {2023}
}
Comments
41 pages, final version; to appear in J. Inst. Math. Jussieu