Closedness of the singular locus and generation for derived categories
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911053098516480 |
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| author | Dey, Souvik Lank, Pat |
| author_facet | Dey, Souvik Lank, Pat |
| contents | This work is concerned with a relationship regarding the closedness of the singular locus of a Noetherian scheme and existence of classical generators in its category of coherent sheaves, associated bounded derived category, and singularity category. Particularly, we extend an observation initially made by Iyengar and Takahashi in the affine context to the global setting. Furthermore, we furnish an example a Noetherian scheme whose bounded derived category admits a classical generator, yet not every finite scheme over it exhibits the same property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19564 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Closedness of the singular locus and generation for derived categories Dey, Souvik Lank, Pat Algebraic Geometry Commutative Algebra Representation Theory 14F08 (primary), 18G80, 13D09, 14B05, 18E10 This work is concerned with a relationship regarding the closedness of the singular locus of a Noetherian scheme and existence of classical generators in its category of coherent sheaves, associated bounded derived category, and singularity category. Particularly, we extend an observation initially made by Iyengar and Takahashi in the affine context to the global setting. Furthermore, we furnish an example a Noetherian scheme whose bounded derived category admits a classical generator, yet not every finite scheme over it exhibits the same property. |
| title | Closedness of the singular locus and generation for derived categories |
| topic | Algebraic Geometry Commutative Algebra Representation Theory 14F08 (primary), 18G80, 13D09, 14B05, 18E10 |
| url | https://arxiv.org/abs/2403.19564 |