The categorical form of Fargues' conjecture for tori
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916347309457408 |
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| author | Zou, Konrad |
| author_facet | Zou, Konrad |
| contents | 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 $π_1(G)_Q$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_13238 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The categorical form of Fargues' conjecture for tori Zou, Konrad Representation Theory Algebraic Geometry Number Theory 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 $π_1(G)_Q$ 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. |
| title | The categorical form of Fargues' conjecture for tori |
| topic | Representation Theory Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2202.13238 |