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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

Moduli of Langlands Parameters

David Helm
  • Fonction : Auteur
Robert Kurinczuk
  • Fonction : Auteur
Gilbert Moss
  • Fonction : Auteur

Résumé

Let $F$ be a nonarchimedean local field of residue characteristic $p$, let $\hat{G}$ be a split connected reductive group over $\mathbb{Z}[1/p]$ with an action of $W_F$, and let $^LG$ denote the semidirect product $\hat{G}\rtimes W_F$. We construct a moduli space of Langlands parameters $W_F \to {^LG}$, and show that it is locally of finite type and flat over $\mathbb{Z}[1/p]$, and that it is a reduced local complete intersection. We give parameterizations of the connected components of this space over algebraically closed fields of characteristic zero and characteristic $\ell\neq p$, as well as of the components over $\overline{\mathbb{Z}}_{\ell}$ and (conjecturally) over $\overline{\mathbb{Z}}[1/p]$. Finally we study the functions on this space that are invariant under conjugation by $\hat{G}$ (or, equivalently, the GIT quotient by $\hat{G}$) and give a complete description of this ring of functions after inverting an explicit finite set of primes depending only on $^LG$.

Dates et versions

hal-03903817 , version 1 (16-12-2022)

Identifiants

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Jean-François Dat, David Helm, Robert Kurinczuk, Gilbert Moss. Moduli of Langlands Parameters. 2022. ⟨hal-03903817⟩
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