Hitchin map for the moduli space of Λ-modules in positive characteristic

D. Alfaya, C. Pauly

Journal of Algebra Vol. 634, pp. 306 - 335

Summary:

Building on Simpson's original definition over the complex numbers, we introduce the notion of restricted sheaf Λ of rings of differential operators on a variety defined over a field of positive characteristic. We define the notion of p-curvature for Λ-modules and the analogue of the Hitchin map on the moduli space of Λ-modules. We show that under certain conditions this Hitchin map descends under the Frobenius map of the underlying variety and we give examples.

Spanish layman's summary:

Introducimos la noción de haz Λ de anillos de operadores diferenciales restringido en una variedad sobre un cuerpo de característica positiva. Definimos la noción de p-curvatura para Λ-módulos y un análogo del morfismo de Hitchin para el moduli de Λ-módulos.

English layman's summary:

We introduce the notion of restricted sheaf Λ of rings of differential operators on a variety over a field of positive characteristic. We define the notion of p-curvature for Λ-modules and an analogue of the Hitchin map on the moduli of Λ-modules.

Keywords: Hitchin map; Lambda-modules; Connections; Higgs bundles; Positive characteristic; Moduli space

JCR Impact Factor and WoS quartile: 0,900 - Q2 (2022)

DOI reference: https://doi.org/10.1016/j.jalgebra.2023.07.012

Published on paper: November 2023.

Published on-line: July 2023.

Citation:
D. Alfaya, C. Pauly, Hitchin map for the moduli space of Λ-modules in positive characteristic. Journal of Algebra. Vol. 634, pp. 306 - 335, November 2023. [Online: July 2023]