On the differentials of the Hochschild-Kostant-Rosenberg spectral sequence
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911506499633152 |
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| author | Mundinger, Joshua |
| author_facet | Mundinger, Joshua |
| contents | The Hochschild-Kostant-Rosenberg theorem implies the existence of a spectral sequence computing the Hochschild homology of a variety in terms of the cohomology of differential forms. When the base field $k$ has characteristic $p>0$, we show that the differentials in this spectral sequence are zero before page $p$; when the variety admits a lift to $W_2(k)$, we give a formula for the differential on page $p$. The formula involves the Bockstein associated to the lift and a $p$th power operation for the Atiyah class. Along the way, we also discuss rudiments of Tannakian reconstruction for derived stacks using the $Θ$-categories of Nuiten and Toën. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01894 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the differentials of the Hochschild-Kostant-Rosenberg spectral sequence Mundinger, Joshua Algebraic Geometry Primary: 13D03, Secondary: 14G17, 16E40 The Hochschild-Kostant-Rosenberg theorem implies the existence of a spectral sequence computing the Hochschild homology of a variety in terms of the cohomology of differential forms. When the base field $k$ has characteristic $p>0$, we show that the differentials in this spectral sequence are zero before page $p$; when the variety admits a lift to $W_2(k)$, we give a formula for the differential on page $p$. The formula involves the Bockstein associated to the lift and a $p$th power operation for the Atiyah class. Along the way, we also discuss rudiments of Tannakian reconstruction for derived stacks using the $Θ$-categories of Nuiten and Toën. |
| title | On the differentials of the Hochschild-Kostant-Rosenberg spectral sequence |
| topic | Algebraic Geometry Primary: 13D03, Secondary: 14G17, 16E40 |
| url | https://arxiv.org/abs/2410.01894 |