TY - JOUR

T1 - Lafforgue pseudocharacters and parities of limits of Galois representations

AU - Berger, Tobias

AU - Weiss, Ariel

N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022/5/1

Y1 - 2022/5/1

N2 - Let F be a CM field with totally real subfield F+ and let π be a C-algebraic cuspidal automorphic representation of the unitary group U(a,b)(AF+), whose archimedean components are discrete series or non-degenerate limit of discrete series representations. We attach to π a Galois representation Rπ:Gal(F¯/F+)→CU(a,b)(Q¯ℓ) such that, for any complex conjugation element c, Rπ(c) is as predicted by the Buzzard–Gee conjecture (Buzzard and Gee, in: Automorphic forms and Galois representa, Cambridge University Press, Cambridge, 2014). As a corollary, we deduce that the Galois representations attached to certain irregular, C-algebraic essentially conjugate self-dual cuspidal automorphic representations of GLn(AF) are odd in the sense of Bellaïche–Chenevier (Compos Math 147(5):1337–1352, 2011).

AB - Let F be a CM field with totally real subfield F+ and let π be a C-algebraic cuspidal automorphic representation of the unitary group U(a,b)(AF+), whose archimedean components are discrete series or non-degenerate limit of discrete series representations. We attach to π a Galois representation Rπ:Gal(F¯/F+)→CU(a,b)(Q¯ℓ) such that, for any complex conjugation element c, Rπ(c) is as predicted by the Buzzard–Gee conjecture (Buzzard and Gee, in: Automorphic forms and Galois representa, Cambridge University Press, Cambridge, 2014). As a corollary, we deduce that the Galois representations attached to certain irregular, C-algebraic essentially conjugate self-dual cuspidal automorphic representations of GLn(AF) are odd in the sense of Bellaïche–Chenevier (Compos Math 147(5):1337–1352, 2011).

UR - http://www.scopus.com/inward/record.url?scp=85105245308&partnerID=8YFLogxK

U2 - 10.1007/s00229-021-01305-7

DO - 10.1007/s00229-021-01305-7

M3 - Article

AN - SCOPUS:85105245308

SN - 0025-2611

VL - 168

SP - 225

EP - 256

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

IS - 1-2

ER -