Locally dualizable modules abound
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917558438854656 |
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| author | Carlson, Jon F. Iyengar, Srikanth B. |
| author_facet | Carlson, Jon F. Iyengar, Srikanth B. |
| contents | It is proved that given any prime ideal $\mathfrak{p}$ of height at least 2 in a countable commutative noetherian ring $A$, there are uncountably many more dualizable objects in the $\mathfrak{p}$-local $\mathfrak{p}$-torsion stratum of the derived category of $A$ than those that are obtained as retracts of images of perfect $A$-complexes. An analogous result is established dealing with the stable module category of the group algebra, over a countable field of positive characteristic $p$, of an elementary abelian $p$-group of rank at least 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02350 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Locally dualizable modules abound Carlson, Jon F. Iyengar, Srikanth B. Commutative Algebra Representation Theory 13D09 (primary), 18G80, 14F08 (secondary It is proved that given any prime ideal $\mathfrak{p}$ of height at least 2 in a countable commutative noetherian ring $A$, there are uncountably many more dualizable objects in the $\mathfrak{p}$-local $\mathfrak{p}$-torsion stratum of the derived category of $A$ than those that are obtained as retracts of images of perfect $A$-complexes. An analogous result is established dealing with the stable module category of the group algebra, over a countable field of positive characteristic $p$, of an elementary abelian $p$-group of rank at least 3. |
| title | Locally dualizable modules abound |
| topic | Commutative Algebra Representation Theory 13D09 (primary), 18G80, 14F08 (secondary |
| url | https://arxiv.org/abs/2401.02350 |