The geometry of permutation modules
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | |
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| _version_ | 1866916853165588480 |
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| author | Balmer, Paul Gallauer, Martin |
| author_facet | Balmer, Paul Gallauer, Martin |
| contents | We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the problem to elementary abelian groups and then by using a twisted form of cohomology to express the spectrum locally in terms of the graded endomorphism ring of the unit. Together, these results yield a classification of thick and of localizing ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_04398 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The geometry of permutation modules Balmer, Paul Gallauer, Martin Representation Theory Category Theory We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the problem to elementary abelian groups and then by using a twisted form of cohomology to express the spectrum locally in terms of the graded endomorphism ring of the unit. Together, these results yield a classification of thick and of localizing ideals. |
| title | The geometry of permutation modules |
| topic | Representation Theory Category Theory |
| url | https://arxiv.org/abs/2307.04398 |