Compatibility of Local and Global Langlands Correspondences
By Richard Taylor, Teruyoshi Yoshida. 2004
152 citations recorded by the source corpus.
We prove the compatibility of local and global Langlands correspondences for GLn, which was proved up to semisimplification in [HT]. More precisely, for the ndimensional l-adic representation Rl(Π) of the Galois group of an imaginary CM-field L attached to a conjugate self-dual regular algebraic cuspidal automorphic representation Π of GLn(AL), which is square integrable at some finite place, we show that Frobenius semisimplification of the restriction of Rl(Π) to the decomposition group of a place v of L not dividing l corresponds to Πv by the local Langlands correspondence. If Πv is square integrable for some finite place v 6 | l we deduce that Rl(Π) is irreducible. We also obtain conditional results in the case v|l.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b0f70f2ecb68318438c60d92a9b4b51d288f6be2
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In Geometry and Topology
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- David Geraghty
- J. Thorne
- Peter Scholze
- Frank Calegari
- Thomas Barnet-Lamb
- Ana Caraiani
- L. Clozel
In Mathematical Physics
- T. Gee
- David Geraghty
- J. Thorne
- Peter Scholze
- Frank Calegari
- Thomas Barnet-Lamb
- Ana Caraiani
- L. Clozel
Citations in the corpus
- Automorphic forms and rational homology 3--spheres (2005, background): “compatibility for GSp4/Q, which is not currently known (though not expected to be too difficult, for example it is now known for GL n [44]).”
- Automorphy for some l-adic lifts of automorphic mod l Galois representations (2008, methodology): “238 RICHARD TAYLOR for instance [ TY ]). Moreover for all but finitely many p there is a Weil–Deligne representation WDp(Vt) of WQ p over Q such that for each prime l � p and each embedding Q � → Q l the Weil–Deligne representation WDp(Vt) is equivalent to the Frobenius semi-simplification WD(Vl,t|G”
- The Sato-Tate conjecture for Hilbert modular forms (2009, unknown): “If K is a nite extension of Qp for some p, we will let recK be the local Langlands correspondence of [ HT01 ], so that if is an irreducible complex admissible representation of GLn(K), then recK( ) is a Weil-Deligne representation of the Weil group WK. If K is an archimedean local eld, we write rec ”
- Monodromy and local-global compatibility for l = p (2012, methodology): “Following the conventions of [Taylor and Yoshida 2007], we call a Weil–Deligne representation pure of weight k if it admits a weight filtration, with all the weights in kCZ, such that the (iterated) monodromy operator induces an isomorphism of the .”