Semi-Bousfield classes and nonmonotone perversities
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918529991704576 |
|---|---|
| author | Herbera, Dolors Hrbek, Michal Gros, Giovanna Le |
| author_facet | Herbera, Dolors Hrbek, Michal Gros, Giovanna Le |
| contents | In the generality of a rigidly-compactly generated tensor triangulated category, we introduce semi-Bousfield classes in terms of the vanishing of the tensor product in positive degrees with respect to a fixed reasonable $t$-structure. We show that semi-Bousfield classes provide a common generalisation of Bousfield classes and compactly generated tensor-compatible $t$-structures. Then we specialise to the setting of the unbounded derived category $\mathcal{D}_{\mathrm{qc}}(X)$ of a Noetherian scheme $X$ and show that the stratification bijection naturally extends to an assignment which takes a (not necessarily monotone) perversity on $X$ to a semi-Bousfield class in $\mathcal{D}_{\mathrm{qc}}(X)$. If $X$ is regular, this assignment constitutes a stratification of the whole semi-Bousfield lattice, while in the singular case, its image consists precisely of those semi-Bousfield classes arising from objects of finite Tor-dimension. Restricting this bijection to monotone perversities recovers the recent classification of compactly generated tensor-compatible $t$-structures of Dubey and Sahoo, (arXiv:2204.05015). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30262 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semi-Bousfield classes and nonmonotone perversities Herbera, Dolors Hrbek, Michal Gros, Giovanna Le Category Theory Commutative Algebra Algebraic Geometry 14A30, 18G80 (primary), 13D09, 14F08, 14B05 In the generality of a rigidly-compactly generated tensor triangulated category, we introduce semi-Bousfield classes in terms of the vanishing of the tensor product in positive degrees with respect to a fixed reasonable $t$-structure. We show that semi-Bousfield classes provide a common generalisation of Bousfield classes and compactly generated tensor-compatible $t$-structures. Then we specialise to the setting of the unbounded derived category $\mathcal{D}_{\mathrm{qc}}(X)$ of a Noetherian scheme $X$ and show that the stratification bijection naturally extends to an assignment which takes a (not necessarily monotone) perversity on $X$ to a semi-Bousfield class in $\mathcal{D}_{\mathrm{qc}}(X)$. If $X$ is regular, this assignment constitutes a stratification of the whole semi-Bousfield lattice, while in the singular case, its image consists precisely of those semi-Bousfield classes arising from objects of finite Tor-dimension. Restricting this bijection to monotone perversities recovers the recent classification of compactly generated tensor-compatible $t$-structures of Dubey and Sahoo, (arXiv:2204.05015). |
| title | Semi-Bousfield classes and nonmonotone perversities |
| topic | Category Theory Commutative Algebra Algebraic Geometry 14A30, 18G80 (primary), 13D09, 14F08, 14B05 |
| url | https://arxiv.org/abs/2605.30262 |