nLab moduli stack of L-parameters




The moduli stack of L-parameters is an algebraic moduli stack that parametrizes L-parameters, which generalize the Weil-Deligne representations for the local Langlands correspondence when the reductive group is not the general linear group GL nGL_n.

In the “classical” \ell-adic case of the local Langlands correspondence, this moduli stack was constructed independently by Dat-Helm-Kurinczuk-Moss (DHKM20), Fargues-Scholze (FarguesScholze21), and Zhu (Zhu20). For the p-adic local Langlands correspondence, the relevant stack has to be the moduli stack of etale (φ,Γ)(\varphi,\Gamma)-modules (also known as the Emerton-Gee stack), constructed by Emerton-Gee (EmertonGee19).

The corresponding notion in the geometric Langlands correspondence is the moduli stack of local systems (recall – e.g. from Deligne 1970 – that local systems on a curve (or any space) give linear representations of its fundamental group, hence are akin to Galois representations).


Last revised on November 27, 2022 at 01:56:06. See the history of this page for a list of all contributions to it.