Singularities and transfer (Q743714)

In a previous paper of the author, in collaboration with \textit{E. Frenkel} and \textit{B. C. Ngô} [Ann. Sci. Math. Qué. 34, No. 2, 199--243 (2010; Zbl 1267.11113)], a program to solve the Langlands functoriality problem is provided. The Langlands functoriality problem suggests a precise relation between automorphic representations of different groups and their \(L\)-groups. The paper under review illustrates Frenkel-Ngô-Langlands' program in the example of the group \(\mathrm{SL}(2)\) for which the definition and the construction of a stable transfer is accomplished carefully and successfully. Finally, the author points out the difficulties to be expected for more general groups, and provides hints to handle some of these difficulties. The text is written in french, and contains a short abstract in english.