Author
Groechenig, M
Wyss, D
Ziegler, P
Last updated
2019-04-17T04:23:23.26+01:00
Abstract
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.
Symplectic ID
973728
Download URL
http://arxiv.org/abs/1810.06739v1
Publication type
Journal Article
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