A filtered Hochschild-Kostant-Rosenberg theorem for real Hochschild homology
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915182945501184 |
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| author | Yang, Lucy |
| author_facet | Yang, Lucy |
| contents | In this paper, we introduce a notion of derived involutive algebras in $ C_2 $-Mackey functors which simultaneously generalize commutative rings with involution and the (non-equivariant) derived algebras of Bhatt--Mathew and Raksit. We show that the $ \infty $-category of derived involutive algebras admits involutive enhancements of the cotangent complexes, de Rham complex, and de Rham cohomology functors; furthermore, their real Hochschild homology is defined. We identify a filtration on the real Hochschild homology of these derived involutive algebras via a universal property and show that its associated graded may be identified with the involutive de Rham complex. Using $ C_2 $-$ \infty $-categories of Barwick--Dotto--Glasman--Nardin--Shah, we show that our filtered real Hochschild homology specializes to the HKR-filtered Hochschild homology considered by Raksit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03024 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A filtered Hochschild-Kostant-Rosenberg theorem for real Hochschild homology Yang, Lucy Algebraic Topology Algebraic Geometry K-Theory and Homology In this paper, we introduce a notion of derived involutive algebras in $ C_2 $-Mackey functors which simultaneously generalize commutative rings with involution and the (non-equivariant) derived algebras of Bhatt--Mathew and Raksit. We show that the $ \infty $-category of derived involutive algebras admits involutive enhancements of the cotangent complexes, de Rham complex, and de Rham cohomology functors; furthermore, their real Hochschild homology is defined. We identify a filtration on the real Hochschild homology of these derived involutive algebras via a universal property and show that its associated graded may be identified with the involutive de Rham complex. Using $ C_2 $-$ \infty $-categories of Barwick--Dotto--Glasman--Nardin--Shah, we show that our filtered real Hochschild homology specializes to the HKR-filtered Hochschild homology considered by Raksit. |
| title | A filtered Hochschild-Kostant-Rosenberg theorem for real Hochschild homology |
| topic | Algebraic Topology Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2503.03024 |