{"paper":{"title":"Complete integrability of the parahoric Hitchin system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP","math.RT"],"primary_cat":"math.AG","authors_text":"David Baraglia, Masoud Kamgarpour, Rohith Varma","submitted_at":"2016-08-18T23:33:26Z","abstract_excerpt":"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, thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05454","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}