an:06266535
Zbl 1310.11062
Chenevier, Ga??tan; Harris, Michael
Construction of automorphic Galois representations. II
EN
Camb. J. Math. 1, No. 1, 53-73 (2013).
00321903
2013
j
11F80 11F85 11F70 11S37 22E55 22E50
Galois representations; automorphic forms; Shimura varieties; eigenvarieties
Let \(F\) be a totally real field and \(K\) a totally imaginary quadratic extension of \(F\). This paper constructs Galois representations associated to certain cuspidal automorphic representations of \(\mathrm{GL}(n,K)\): Let \(\Pi\) be a cuspidal automorphic representation of \(\mathrm{GL}(n,K)\) that is cohomological and `conjugate self-dual'. Then there exists a semi-simple continuous Galois representation \(\rho_{\iota,\Pi} : G_K \rightarrow \mathrm{GL}(n,\overline{\mathbb Q}_p)\) associated to \(\Pi\) (where \(\iota\) is are choices of embeddings of \(\overline{\mathbb Q}\) into \(\overline{\mathbb Q}_p\) and \(\mathbb C\)) which satisfying some local compatibility conditions at places \(v\) not dividing \(p\) and as well as dividing \(p\). This main result is achieved by constructing missing Galois representations for even degree \(F\) by \(p\)-adic approximation and has applications to automorphy lifting theorems.
This is a revised version of the articles ``Endoscopic transfer'', and ``Construction of automorphic Galois representations. I'' by \textit{L. Clozel}, \textit{M. Harris} and \textit{J.-P. Labesse} [Stabilization of the trace formula, Shimura varieties, and arithmetic applications. Volume 1: On the stabilization of the trace formula. Somerville, MA: International Press, 475--496, 497--523 (2011; Zbl 1255.11027)] and of an earlier version of the present article [\url{http://fa.institut.math.jussieu.fr/node/45}].
Imin Chen (Burnaby)
Zbl 1255.11027