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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2209.08732 |
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| _version_ | 1866910019411247104 |
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| author | Lyu, Shiji Murayama, Takumi |
| author_facet | Lyu, Shiji Murayama, Takumi |
| contents | We establish the relative minimal model program with scaling for locally projective morphisms of quasi-excellent algebraic spaces admitting dualizing complexes, quasi-excellent formal schemes admitting dualizing complexes, semianalytic germs of complex analytic spaces, rigid analytic spaces, Berkovich spaces, and adic spaces locally of weakly finite type over a field, all in equal characteristic zero. To do so, we prove finite generation of relative adjoint rings associated to projective morphisms of such spaces using the strategy of Cascini and Lazić and the generalization of the Kawamata-Viehweg vanishing theorem to the scheme setting recently established by the second author. To prove these results uniformly, we prove GAGA theorems for Grothendieck duality and dualizing complexes to reduce to the algebraic case. In addition, we apply our methods to establish the relative minimal model program with scaling for spaces of the form above in dimensions $\le 3$ in positive and mixed characteristic, and to show that one can run the relative minimal model program with scaling for complex analytic spaces without shrinking the base at each step. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_08732 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero Lyu, Shiji Murayama, Takumi Algebraic Geometry 14E30 (Primary) 13F40, 14G22, 32C15, 14J30 (Secondary) We establish the relative minimal model program with scaling for locally projective morphisms of quasi-excellent algebraic spaces admitting dualizing complexes, quasi-excellent formal schemes admitting dualizing complexes, semianalytic germs of complex analytic spaces, rigid analytic spaces, Berkovich spaces, and adic spaces locally of weakly finite type over a field, all in equal characteristic zero. To do so, we prove finite generation of relative adjoint rings associated to projective morphisms of such spaces using the strategy of Cascini and Lazić and the generalization of the Kawamata-Viehweg vanishing theorem to the scheme setting recently established by the second author. To prove these results uniformly, we prove GAGA theorems for Grothendieck duality and dualizing complexes to reduce to the algebraic case. In addition, we apply our methods to establish the relative minimal model program with scaling for spaces of the form above in dimensions $\le 3$ in positive and mixed characteristic, and to show that one can run the relative minimal model program with scaling for complex analytic spaces without shrinking the base at each step. |
| title | The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero |
| topic | Algebraic Geometry 14E30 (Primary) 13F40, 14G22, 32C15, 14J30 (Secondary) |
| url | https://arxiv.org/abs/2209.08732 |