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arXiv · 1608.05454

Complete integrability of the parahoric Hitchin system

David Baraglia·Masoud Kamgarpour·Rohith Varma
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Abstract

Let $\mathcal{G}$ be a parahoric group scheme over a complex projective curve $X$ of genus greater than one. Let $\mathrm{Bun}_{\mathcal{G}}$ denote the moduli stack of $\mathcal{G}$-torsors on $X$. We prove several results concerning the Hitchin map on $T^*\!\mathrm{Bun}_{\mathcal{G}}$. We first show that the parahoric analogue of the global nilpotent cone is isotropic and use this to prove that $\mathrm{Bun}_{\mathcal{G}}$ is "very good" in the sense of Beilinson-Drinfeld. We then prove that the parahoric Hitchin map is a Poisson map whose generic fibres are abelian varieties. Together, these results imply that the parahoric Hitchin map is a completely integrable system.

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David Baraglia, Masoud Kamgarpour, Rohith Varma. 2017-03-15. Complete integrability of the parahoric Hitchin system. https://doi.org/10.1093/imrn%2Frnx313

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