Categorical characterizations of regularity for algebraic stacks
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917416443838464 |
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| author | De Deyn, Timothy Lank, Pat Rahul, Kabeer Manali Peng, Fei |
| author_facet | De Deyn, Timothy Lank, Pat Rahul, Kabeer Manali Peng, Fei |
| contents | For a Noetherian scheme $X$ of finite Krull dimension, Neeman recently established two characterizations of the regularity of $X$ using strong generators and bounded $t$-structures on $\operatorname{Perf}(X)$. In this note, we obtain variants of Neeman's results for large classes of Noetherian algebraic stacks. An important intermediate step is the fact that $X$ is regular if and only if $\operatorname{Perf}(X)=D_{\operatorname{coh}}^b(X)$, which we establish for Noetherian algebraic stacks. Our approach also yields a criterion for the existence of classical generators for the bounded derived categories of coherent sheaves on algebraic stacks, generalizing previous results for commutative rings and schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02813 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Categorical characterizations of regularity for algebraic stacks De Deyn, Timothy Lank, Pat Rahul, Kabeer Manali Peng, Fei Algebraic Geometry Commutative Algebra 14A30 (primary), 14F08, 14A20, 14D23 For a Noetherian scheme $X$ of finite Krull dimension, Neeman recently established two characterizations of the regularity of $X$ using strong generators and bounded $t$-structures on $\operatorname{Perf}(X)$. In this note, we obtain variants of Neeman's results for large classes of Noetherian algebraic stacks. An important intermediate step is the fact that $X$ is regular if and only if $\operatorname{Perf}(X)=D_{\operatorname{coh}}^b(X)$, which we establish for Noetherian algebraic stacks. Our approach also yields a criterion for the existence of classical generators for the bounded derived categories of coherent sheaves on algebraic stacks, generalizing previous results for commutative rings and schemes. |
| title | Categorical characterizations of regularity for algebraic stacks |
| topic | Algebraic Geometry Commutative Algebra 14A30 (primary), 14F08, 14A20, 14D23 |
| url | https://arxiv.org/abs/2504.02813 |