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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Geometric stabilisation via $p$-adic integration
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by Michael Groechenig, Dimitri Wyss and Paul Ziegler HTML | PDF
J. Amer. Math. Soc. 33 (2020), 807-873 Request permission


In this article we give a new proof of Ngô’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.
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Additional Information
  • Michael Groechenig
  • Affiliation: Department of Mathematical and Computational Sciences, University of Toronta at Mississauga, 3359 Mississauga Rd N., Ontario Canada
  • Address at time of publication: Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada M5S 2E4
  • MR Author ID: 1058689
  • Email:
  • Dimitri Wyss
  • Affiliation: Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
  • MR Author ID: 1245166
  • Email:
  • Paul Ziegler
  • Affiliation: Mathematical Institute, University of Oxford, Oxford, United Kingdom
  • Address at time of publication: Department of Mathematics, Technische Universität München, Munich, Germany
  • MR Author ID: 940936
  • Email:
  • Received by editor(s): November 8, 2018
  • Received by editor(s) in revised form: October 28, 2019
  • Published electronically: June 15, 2020
  • Additional Notes: The first author was funded by a Marie Skłodowska-Curie fellowship: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 701679.
    The second author was supported by the Foundation Sciences Mathématiques de Paris, as well as a public grant overseen by the French National Research Agency (ANR) as part of the Investissements d’avenir program (reference: ANR-10-LABX-0098) and also by ANR-15-CE40-0008 (Défigéo).
    The third author was supported by the Swiss National Science Foundation.
  • © Copyright 2020 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 33 (2020), 807-873
  • MSC (2010): Primary 11S37, 11S80, 14H60, 20G40, 14D24
  • DOI:
  • MathSciNet review: 4127904