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Non-basic rigid packets for discrete $L$-parameters
Number Theory · Submitted 25 Aug 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Motivated by the recent work of Bertoloni Meli--Oi on the $B(G)$-parametrization of the local Langlands conjectures, our main application is to extend the basic rigid refined local Langlands conjectures for a discrete $L$-parameter $\phi$ of a quasi-split connected reductive group $G$.
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The abstract, sentence by sentence
This article initiates the study of non-basic rigid inner forms over $p$-adic local fields, extending the basic theory developed by Kaletha. Motivated by the recent work of Bertoloni Meli--Oi on the $B(G)$-parametrization of the local Langlands conjectures, our main application is to extend the basic rigid refined local Langlands conjectures for a discrete $L$-parameter $\phi$ of a quasi-split connected reductive group $G$. The packets of our extended construction are Weyl orbits of representations of inner forms of twisted Levi subgroups $N$ of $G$ for which $\phi$ factors through a member of the canonical $L$-embeddings $^{L}N_{\pm} \to {^{L}G}$ constructed by Kaletha.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This article initiates the study of non-basic rigid inner forms over $p$-adic local fields, extending the basic theory developed by Kaletha. | contribution 0.99 | 0.86 | 0.08 | asserted 1.00 |
| s1 | Motivated by the recent work of Bertoloni Meli--Oi on the $B(G)$-parametrization of the local Langlands conjectures, our main application is to extend the basic rigid refined local Langlands conjectures for a discrete $L$-parameter $\phi$ of a quasi-split connected reductive group $G$. | contribution 0.87 | 0.64 | 0.52 | asserted 0.98 |
| s2 | The packets of our extended construction are Weyl orbits of representations of inner forms of twisted Levi subgroups $N$ of $G$ for which $\phi$ factors through a member of the canonical $L$-embeddings $^{L}N_{\pm} \to {^{L}G}$ constructed by Kaletha. | contribution 0.65 | 0.86 | 0.28 | asserted 1.00 |
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The paper
Original abstract
This article initiates the study of non-basic rigid inner forms over $p$-adic local fields, extending the basic theory developed by Kaletha. Motivated by the recent work of Bertoloni Meli--Oi on the $B(G)$-parametrization of the local Langlands conjectures, our main application is to extend the basic rigid refined local Langlands conjectures for a discrete $L$-parameter $\phi$ of a quasi-split connected reductive group $G$. The packets of our extended construction are Weyl orbits of representations of inner forms of twisted Levi subgroups $N$ of $G$ for which $\phi$ factors through a member of the canonical $L$-embeddings $^{L}N_{\pm} \to {^{L}G}$ constructed by Kaletha.
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What this paper does with the arXiv papers it cites
What it cites · 21 sentences without a confident label
Uses the method or tool of 1 paper
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This proof will mostly follow the arguments of [ref] .
On L-embeddings and double covers of tori over local fields · The basic conjectures · 0.94
Cites as background 4 papers
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Because the details of the construction are not critical for our application, we refer the reader to [ref] for more details.
On L-embeddings and double covers of tori over local fields · $L$-embeddings from twisted Levi subgroups · 0.97
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Perhaps the most prominent example of this phenomenon is Yu's construction of supercuspidal representations [ref] and Kaletha's parametrization of most of them [ref] .
Supercuspidal L-packets · Introduction · 0.88
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The sets $B(G)$ and $B(G)_bas$ also appear in the geometry of the space $Bun_G$, the moduli stack of $G$-bundles on the Fargues–Fontaine curve, which underlies Fargues and Scholze's geometrization of the local Langlands correspondence [ref] .
Geometrization of the local Langlands correspondence · The $B(G)$ local Langlands conjectures · 0.97
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