An approach to the characterization of the local Langlands correspondence

Scholze and Shin [J. Amer. Math. Soc. 26 (2013), pp. 261–294] gave a conjectural formula relating the traces on automorphic Galois sides of local Langlands correspondence. Their work generalized an earlier Scholze, which he used to give new proof conjecture for G mathvariant="normal">L n \mathrm {GL}_n . Unlike case , existence non-singleton alttext="upper L"> L encoding="application/x-tex">L -packets more general reductive groups constitutes serious representation-theoretic obstruction proving that such uniquely characterizes We show how overcome this problem, demonstrate Scholze–Shin equation is enough, together with other standard desiderata, characterize correspondence discrete parameters.