Derived graded modules
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866913000169930752 |
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| author | Ishizuka, Ryo Yoshikawa, Shou |
| author_facet | Ishizuka, Ryo Yoshikawa, Shou |
| contents | We introduce the notion of the $\infty$-category of (complete) derived $G$-graded modules over a $G$-graded ring $R$ for a torsion-free abelian group $G$, and we study its foundational properties. Moreover, we prove a categorical equivalence between (complete) derived $G$-graded modules over $R$ and derived (formal) comodules over a certain comonad constructed from the group ring $R[G]$ of $G$ over $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19164 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Derived graded modules Ishizuka, Ryo Yoshikawa, Shou Commutative Algebra Algebraic Geometry We introduce the notion of the $\infty$-category of (complete) derived $G$-graded modules over a $G$-graded ring $R$ for a torsion-free abelian group $G$, and we study its foundational properties. Moreover, we prove a categorical equivalence between (complete) derived $G$-graded modules over $R$ and derived (formal) comodules over a certain comonad constructed from the group ring $R[G]$ of $G$ over $R$. |
| title | Derived graded modules |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2601.19164 |