On proper splinters in positive characteristic
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917200148824064 |
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| author | Krah, Johannes Vial, Charles |
| author_facet | Krah, Johannes Vial, Charles |
| contents | While the splinter property is a local property for Noetherian schemes in characteristic zero, Bhatt observed that it imposes strong conditions on the global geometry of proper schemes in positive characteristic. We show that if a proper scheme over a field of positive characteristic is a splinter, then its Nori fundamental group scheme is trivial and its Kodaira dimension is negative. In another direction, Bhatt also showed that any splinter in positive characteristic is a derived splinter. We ask whether the splinter property is a derived invariant for projective varieties in positive characteristic and give a positive answer for normal Gorenstein projective varieties with big anticanonical divisor. We also show that global F-regularity is a derived invariant for normal Gorenstein projective varieties in positive characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02511 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On proper splinters in positive characteristic Krah, Johannes Vial, Charles Algebraic Geometry 14G17, 14F35, 14L30, 14F08, 14J17, 14J26, 14E05 While the splinter property is a local property for Noetherian schemes in characteristic zero, Bhatt observed that it imposes strong conditions on the global geometry of proper schemes in positive characteristic. We show that if a proper scheme over a field of positive characteristic is a splinter, then its Nori fundamental group scheme is trivial and its Kodaira dimension is negative. In another direction, Bhatt also showed that any splinter in positive characteristic is a derived splinter. We ask whether the splinter property is a derived invariant for projective varieties in positive characteristic and give a positive answer for normal Gorenstein projective varieties with big anticanonical divisor. We also show that global F-regularity is a derived invariant for normal Gorenstein projective varieties in positive characteristic. |
| title | On proper splinters in positive characteristic |
| topic | Algebraic Geometry 14G17, 14F35, 14L30, 14F08, 14J17, 14J26, 14E05 |
| url | https://arxiv.org/abs/2309.02511 |