On non-commutative Euler systems, I: preliminaries on `det' and `Fit'
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866915494375718912 |
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| author | Burns, David Sano, Takamichi |
| author_facet | Burns, David Sano, Takamichi |
| contents | We extend some classical constructions in commutative algebra to the setting of modules over orders in (non-commutative) semisimple algebras. Our theory incorporates, inter alia, `reduced' versions of the notions of higher Fitting invariants and higher exterior powers and of the Grothendieck-Knudsen-Mumford determinant functor on perfect complexes. In a companion article, these results are used to develop a theory of non-commutative Euler systems for $p$-adic representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_10564 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On non-commutative Euler systems, I: preliminaries on `det' and `Fit' Burns, David Sano, Takamichi Number Theory We extend some classical constructions in commutative algebra to the setting of modules over orders in (non-commutative) semisimple algebras. Our theory incorporates, inter alia, `reduced' versions of the notions of higher Fitting invariants and higher exterior powers and of the Grothendieck-Knudsen-Mumford determinant functor on perfect complexes. In a companion article, these results are used to develop a theory of non-commutative Euler systems for $p$-adic representations. |
| title | On non-commutative Euler systems, I: preliminaries on `det' and `Fit' |
| topic | Number Theory |
| url | https://arxiv.org/abs/2004.10564 |