Galois descent of splendid Rickard equivalences for blocks of $p$-nilpotent groups
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914142938464256 |
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| author | Miller, Sam K. |
| author_facet | Miller, Sam K. |
| contents | We strengthen the results of Boltje and Yilmaz regarding the Galois descent of equivalences of blocks of $p$-nilpotent groups and a result of Kessar and Linckelmann regarding Galois descent of splendid Rickard equivalences for blocks with compatible Galois stabilizers. A more general descent criteria for chain complexes is proven along the way, which requires the adaptation of a theorem of Reiner for chain complexes. This verifies Kessar and Linckelmann's refinement of Broué's abelian defect group conjecture for blocks of $p$-nilpotent groups with abelian Sylow $p$-subgroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16061 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Galois descent of splendid Rickard equivalences for blocks of $p$-nilpotent groups Miller, Sam K. Group Theory Rings and Algebras Representation Theory 20C20, 20J05, 20C05, 20F19, 18G35 We strengthen the results of Boltje and Yilmaz regarding the Galois descent of equivalences of blocks of $p$-nilpotent groups and a result of Kessar and Linckelmann regarding Galois descent of splendid Rickard equivalences for blocks with compatible Galois stabilizers. A more general descent criteria for chain complexes is proven along the way, which requires the adaptation of a theorem of Reiner for chain complexes. This verifies Kessar and Linckelmann's refinement of Broué's abelian defect group conjecture for blocks of $p$-nilpotent groups with abelian Sylow $p$-subgroup. |
| title | Galois descent of splendid Rickard equivalences for blocks of $p$-nilpotent groups |
| topic | Group Theory Rings and Algebras Representation Theory 20C20, 20J05, 20C05, 20F19, 18G35 |
| url | https://arxiv.org/abs/2405.16061 |