Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/122564
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Type: Journal article
Title: Complete Integrability of the Parahoric Hitchin System
Author: Baraglia, D.
Kamgarpour, M.
Varma, R.
Citation: International Mathematics Research Notices, 2019; 2019(21):6499-6528
Publisher: Oxford University Press
Issue Date: 2019
ISSN: 1073-7928
1687-0247
Statement of
Responsibility: 
David Baraglia, Masoud Kamgarpour, Rohith Varma
Abstract: Let G be a parahoric group scheme over a complex projective curve X of genus greater than one. Let BunG denote the moduli stack of G-torsors on X. We prove several results concerning the Hitchin map on TBunG⁠. We first show that the parahoric analogue of the global nilpotent cone is isotropic and use this to prove that BunG 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.
Rights: © The Author(s) 2018. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.
DOI: 10.1093/imrn/rnx313
Appears in Collections:Aurora harvest 4
Mathematical Sciences publications

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