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Beijing notes on the categorical local Langlands conjecture

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arxiv 2310.04533 v2 pith:3ZBXQENH submitted 2023-10-06 math.NT math.AGmath.RT

David Hansen This is my paper · ORCID
classification math.NTmath.AGmath.RT
keywords categoricalconjecturelanglandslocalsidesomet-structureautomorphic
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We formulate some refinements and complements to the categorical local Langlands conjecture of Fargues-Scholze. In particular, we state the expected compatibilities with Eisenstein series and duality, and explain some of their consequences. We also begin the process of matching t-structures on both sides. Notably, we introduce the so-called hadal t-structure on the automorphic side, which has good finiteness properties, and which conjecturally matches with a suitable perverse coherent t-structure on the spectral side.

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Cited by 1 Pith paper

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  1. Stability of Elliptic Fargues-Scholze $L$-packets

    math.RT 2024-12 conditional novelty 7.0 of 10

    For elliptic Fargues-Scholze L-parameters, a non-zero integer combination of Harish-Chandra characters of packet members is stable under stable conjugacy.

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