Galois representations associated with unitary groups over \(\mathbb Q\) (Q1950991)

The author of the paper under review proves that a cuspidal automorphic representation \(\pi\) of \(\mathrm{GU}(a,b)/\mathbb Q\) with archimedean component in a discrete series and regular has an associated \((a+b)\)-dimensional \(p\)-adic Galois representation with Frobenius eigenvalues given by the local base change parameters for all primes \(\ell\) such that \(\pi\) and \(\mathrm{GU}(a,b)\) are unramified. He uses the results of \textit{S. Morel} [On the cohomology of certain noncompact Shimura varieties. Princeton, NJ: Princeton University Press (2010; Zbl 1233.11069)] and \textit{S. W. Shin} [Ann. Math. (2) 173, No. 3, 1645--1741 (2011; Zbl 1269.11053)] to deduce the results. The work of the paper under review is motivated by the author's joint work with \textit{E. Urban} proving the Iwasawa-Greenberg conjecture for large class of modular forms [``The Iwasawa main conjectures for \(\mathrm{GL}_{2}\)'', Preprint (2010), {\url{http://www.math.columbia.edu/~urban/eurp/MC.pdf}}].