Geometric stabilisation via p-adic integration
| Autor: | Groechenig, Michael, Wyss, Dimitri, Ziegler, Paul |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this article we give a new proof of Ng\^o's Geometric Stabilisation Theorem, which implies the Fundamental Lemma. This is a statement which relates the cohomology of Hitchin fibres for a quasi-split reductive group scheme $G$ to the cohomology of Hitchin fibres for the endoscopy groups $H_{\kappa}$. Our proof avoids the Decomposition and Support Theorem, instead the argument is based on results for $p$-adic integration on coarse moduli spaces of Deligne-Mumford stacks. Along the way we establish a description of the inertia stack of the (anisotropic) moduli stack of $G$-Higgs bundles in terms of endoscopic data, and extend duality for generic Hitchin fibres of Langlands dual group schemes to the quasi-split case. Comment: 51 pages |
| Databáze: | arXiv |
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