Descent conditions for generation in derived categories
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911824601939968 |
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| author | Lank, Pat |
| author_facet | Lank, Pat |
| contents | This work establishes a condition that determines when strong generation in the bounded derived category of a Noetherian $J\textrm{-}2$ scheme is preserved by the derived pushforward of a proper morphism. Consequently, we can produce upper bounds on the Rouquier dimension of the bounded derived category, and applications concerning affine varieties are studied. In the process, a necessary and sufficient constraint is observed for when a tensor-exact functor between rigidly compactly generated tensor triangulated categories preserves strong $\oplus$-generators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08080 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Descent conditions for generation in derived categories Lank, Pat Algebraic Geometry Commutative Algebra 14F08 (primary), 14A30, 13D09, 18G80 This work establishes a condition that determines when strong generation in the bounded derived category of a Noetherian $J\textrm{-}2$ scheme is preserved by the derived pushforward of a proper morphism. Consequently, we can produce upper bounds on the Rouquier dimension of the bounded derived category, and applications concerning affine varieties are studied. In the process, a necessary and sufficient constraint is observed for when a tensor-exact functor between rigidly compactly generated tensor triangulated categories preserves strong $\oplus$-generators. |
| title | Descent conditions for generation in derived categories |
| topic | Algebraic Geometry Commutative Algebra 14F08 (primary), 14A30, 13D09, 18G80 |
| url | https://arxiv.org/abs/2308.08080 |