Cartier duality via Mittag-Leffler modules
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909964656705536 |
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| author | Arinkin, Dima Mundinger, Joshua |
| author_facet | Arinkin, Dima Mundinger, Joshua |
| contents | We construct the Cartier duality equivalence for affine commutative group schemes $G$ whose coordinate ring is a flat Mittag-Leffler module over an arbitrary base ring $R$. The dual $G^\vee$ of $G$ turns out to be an ind-finite ind-scheme over $R$. When $R$ is Noetherian and admits a dualizing complex, we construct a Fourier-Mukai transform between quasicoherent derived categories of $G$ and of $BG^\vee$ and also between those of $G^\vee$ and $BG$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13856 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cartier duality via Mittag-Leffler modules Arinkin, Dima Mundinger, Joshua Algebraic Geometry Primary: 14L15, Secondary: 14L05, 14F08 We construct the Cartier duality equivalence for affine commutative group schemes $G$ whose coordinate ring is a flat Mittag-Leffler module over an arbitrary base ring $R$. The dual $G^\vee$ of $G$ turns out to be an ind-finite ind-scheme over $R$. When $R$ is Noetherian and admits a dualizing complex, we construct a Fourier-Mukai transform between quasicoherent derived categories of $G$ and of $BG^\vee$ and also between those of $G^\vee$ and $BG$. |
| title | Cartier duality via Mittag-Leffler modules |
| topic | Algebraic Geometry Primary: 14L15, Secondary: 14L05, 14F08 |
| url | https://arxiv.org/abs/2512.13856 |