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    Thorne, Jack A. 2016. A 2-adic automorphy lifting theorem for unitary groups over CM fields. Mathematische Zeitschrift,


    Arias-de-Reyna, Sara Dieulefait, Luis V. Shin, Sug Woo and Wiese, Gabor 2015. Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties. Mathematische Annalen, Vol. 361, Issue. 3-4, p. 909.


    Patrikis, Stefan 2015. On the sign of regular algebraic polarizable automorphic representations. Mathematische Annalen, Vol. 362, Issue. 1-2, p. 147.


    Barnet-Lamb, Thomas Gee, Toby Geraghty, David and Taylor, Richard 2014. Potential automorphy and change of weight. Annals of Mathematics, Vol. 179, Issue. 2, p. 501.


    GEE, TOBY and KISIN, MARK 2014. THE BREUIL–MÉZARD CONJECTURE FOR POTENTIALLY BARSOTTI–TATE REPRESENTATIONS. Forum of Mathematics, Pi, Vol. 2,


    Mok, Chung Pang 2014. Galois representations attached to automorphic forms on over fields. Compositio Mathematica, Vol. 150, Issue. 04, p. 523.


    Chenevier, Gaëtan 2013. Sur la densité des représentations cristallines de $$\text{ Gal}(\overline{\mathbb Q }_p/\mathbb Q _p)$$. Mathematische Annalen, Vol. 355, Issue. 4, p. 1469.


    Taylor, Richard 2012. The image of complex conjugation inl-adic representations associated to automorphic forms. Algebra & Number Theory, Vol. 6, Issue. 3, p. 405.


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The sign of Galois representations attached to automorphic forms for unitary groups

  • Joël Bellaïche (a1) and Gaëtan Chenevier (a2)
  • DOI: http://dx.doi.org/10.1112/S0010437X11005264
  • Published online: 27 July 2011
Abstract
Abstract

Let K be a CM number field and GK its absolute Galois group. A representation of GK is said to be polarized if it is isomorphic to the contragredient of its outer complex conjugate, up to a twist by a power of the cyclotomic character. Absolutely irreducible polarized representations of GK have a sign ±1, generalizing the fact that a self-dual absolutely irreducible representation is either symplectic or orthogonal. If Π is a regular algebraic, polarized, cuspidal automorphic representation of GLn(𝔸K), and if ρ is a p-adic Galois representation attached to Π, then ρ is polarized and we show that all of its polarized irreducible constituents have sign +1 . In particular, we determine the orthogonal/symplectic alternative for the Galois representations associated to the regular algebraic, essentially self-dual, cuspidal automorphic representations of GLn (𝔸F) when F is a totally real number field.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[Car94]H. Carayol , Formes modulaires et représentations galoisiennes à valeurs dans un anneau local complet, in p-adic monodromy and the Birch and Swinnerton-Dyer conjecture, Contemporary Mathematics, vol. 165 (American Mathematical Society, Providence, RI, 1994), 213237.

[CR10]G. Chenevier and D. Renard , On the vanishing of some non semisimple orbital integrals, Expo. Math. 28 (2010), 276289.

[CHT08]L. Clozel , M. Harris and R. Taylor , Automorphy for some l-adic lifts of automorphic mod l representations, Publ. Math. Inst. Hautes Études Sci. 108 (2008), 1181.

[Eme06]M. Emerton , On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms, Invent. Math. 164 (2006), 184.

[Shi11]S.-W. Shin , Galois representations arising from some compact Shimura varieties, Ann. of Math. (2) 173 (2011), 16451741.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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