Duality between Cartier crystals and perverse $\mathbb{F}_p$-sheaves, and application to generic vanishing
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866918059547033600 |
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| author | Baudin, Jefferson |
| author_facet | Baudin, Jefferson |
| contents | We show that on any Noetherian $F$-finite $\mathbb{F}_p$-scheme, there is an anti-equivalence of categories between Cartier crystals and étale perverse $\mathbb{F}_p$-sheaves, commuting with derived proper pushforwards. We use this duality to construct an upper shriek functor for Cartier crystals, and give new proofs of Kashiwara's equivalence and the finite length of Cartier crystals. Finally, we deduce a generic vanishing statement for perverse $\overline{\mathbb{F}}_p$-sheaves on abelian varieties of characteristic $p > 0$, reminiscent of the characteristic zero and $l$-adic statements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_05378 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Duality between Cartier crystals and perverse $\mathbb{F}_p$-sheaves, and application to generic vanishing Baudin, Jefferson Algebraic Geometry 14G17, 13A35, 14K99 We show that on any Noetherian $F$-finite $\mathbb{F}_p$-scheme, there is an anti-equivalence of categories between Cartier crystals and étale perverse $\mathbb{F}_p$-sheaves, commuting with derived proper pushforwards. We use this duality to construct an upper shriek functor for Cartier crystals, and give new proofs of Kashiwara's equivalence and the finite length of Cartier crystals. Finally, we deduce a generic vanishing statement for perverse $\overline{\mathbb{F}}_p$-sheaves on abelian varieties of characteristic $p > 0$, reminiscent of the characteristic zero and $l$-adic statements. |
| title | Duality between Cartier crystals and perverse $\mathbb{F}_p$-sheaves, and application to generic vanishing |
| topic | Algebraic Geometry 14G17, 13A35, 14K99 |
| url | https://arxiv.org/abs/2306.05378 |