On the computation of the vanishing locus of a finitely presented functor
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910985401401344 |
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| author | Posur, Sebastian |
| author_facet | Posur, Sebastian |
| contents | We discuss invariants which are helpful for the computation of the vanishing locus of a finitely presented functor $\mathcal{G}$, i.e., the set of points in the Ziegler spectrum on which $\mathcal{G}$ vanishes. These invariants are: the rank of $\mathcal{G}$, the supports of its co- and contravariant defect, and the class of $\mathcal{G}$ in the Grothendieck group of the category of finitely presented functors. We show that these invariants determine the vanishing locus in the case of a finitely presented functor over a Dedekind domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10524 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the computation of the vanishing locus of a finitely presented functor Posur, Sebastian Category Theory Primary 18E10, Secondary 93C05 We discuss invariants which are helpful for the computation of the vanishing locus of a finitely presented functor $\mathcal{G}$, i.e., the set of points in the Ziegler spectrum on which $\mathcal{G}$ vanishes. These invariants are: the rank of $\mathcal{G}$, the supports of its co- and contravariant defect, and the class of $\mathcal{G}$ in the Grothendieck group of the category of finitely presented functors. We show that these invariants determine the vanishing locus in the case of a finitely presented functor over a Dedekind domain. |
| title | On the computation of the vanishing locus of a finitely presented functor |
| topic | Category Theory Primary 18E10, Secondary 93C05 |
| url | https://arxiv.org/abs/2503.10524 |