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The categorical form of Fargues' conjecture for tori

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arxiv 2202.13238 v2 pith:H5D4ZZ4G submitted 2022-02-26 math.RT math.AGmath.NT

Konrad Zou This is my paper · ORCID
classification math.RTmath.AGmath.NT
keywords proveactioncaseconjecturegrouphomologytoriadditionally
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abstract

We prove the main conjecture of arXiv:2102.13459 for integral coefficients in the case of tori and prove that it is t-exact. Along the way we prove that the spectral action as constructed in that manuscript is compatible with the action of the excursion algebra and preserves the grading by $\pi_1(G)_Q$ on both sides. We additionally develop a (non-solidified) version of condensed group (co)homology and show that many constructions from classical group (co)homology extend to that case.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  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.

  2. Open Condensed Subgroups and Mackey's Formula

    math.CT 2024-12 conditional novelty 6.0 of 10

    Condensed analogues of Mackey's formula and related restriction-induction results hold for open subgroups of condensed groups.

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