Skip to content
DraconiticResearch
Search Sources API
201,818 studies31 sourcesUpdated 27 min ago
PreprintarXiv licencearXiv

Endoscopic description of the local Langlands correspondence for G2

  • Yugo Takanashi
Open at sourcePDFDOICite

Abstract

We prove that the L-packets for p-adic G2 constructed by Gan and Savin satisfy the endoscopic character identities. In the course of the proof, we also prove twisted endoscopic character identities for functorial lifts from G2 to PGSO8 with triality. As a byproduct, we also prove a global multiplicity formula for the discrete automorphic spectrum of G2 coming from the cuspidal automorphic spectrum of PGL3.

Related

  1. The 3-adic Steinberg block and a categorical 3-adic local Langlands correspondence for GL2(ℚ3)
    CJ Dowd
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Supercuspidal blocks and the local Langlands correspondence
    Noriyuki Abe, Kazuma Ohara
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. A conjectural construction of Arthur packets in Fargues-Scholze's categorical local Langlands correspondence
    Geo Kam-Fai Tam
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. A geometric Jacquet--Langlands correspondence for Shimura varieties
    Pol van Hoften, Jack Sempliner
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Block decompositions in the p-adic Langlands correspondence
    Daniel Le, Matthias Strauch, Zichuan Wang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{takanashi2026endoscopic,
  title = {{Endoscopic description of the local Langlands correspondence for $\mathrmG_2$}},
  author = {Yugo Takanashi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19439},
  eprint = {2609.19439},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19439},
}
RIS
TY  - UNPB
TI  - Endoscopic description of the local Langlands correspondence for G_2
AU  - Yugo Takanashi
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.19439
UR  - https://arxiv.org/abs/2609.19439
AB  - We prove that the L-packets for p-adic G_2 constructed by Gan and Savin satisfy the endoscopic character identities. In the course of the proof, we also prove twisted endoscopic character identities for functorial lifts from G_2 to PGSO_8 with triality. As a byproduct, we also prove a global multiplicity formula for the discrete automorphic spectrum of G_2 coming from the cuspidal automorphic spectrum of PGL_3.
ER  -