THE HITCHIN CONNECTION IN ARBITRARY CHARACTERISTIC. (11th January 2023)

• Record Type: Journal Article
• Authors: Pauly, Christian; Martens, Johan; Bolognesi, Michele; Baier, Thomas
• Is Part Of: Journal of the Institute of Mathematics of Jussieu. Volume 22:Number 1(2023)
• Page Start: 449
• Page End: 492
• Publication Date: 2023-01-11
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S1474748022000196
• Languages: English
• ISSNs: 1474-7480

Abstract

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.