Hitchin map for the moduli space of $\Lambda$-modules in positive characteristic

David Alfaya; Christian Pauly

doi:10.1016/j.jalgebra.2023.07.012

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arXiv · 2303.02359

Hitchin map for the moduli space of $\Lambda$-modules in positive characteristic

David Alfaya·Christian Pauly

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Abstract

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

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BibTeX RIS

David Alfaya, Christian Pauly. 2023-03-04. Hitchin map for the moduli space of $\Lambda$-modules in positive characteristic. https://doi.org/10.1016/j.jalgebra.2023.07.012

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