Almost Coherence of Higher Direct Images
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913652447117312 |
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| author | He, Tongmu |
| author_facet | He, Tongmu |
| contents | For a flat proper morphism of finite presentation between schemes with almost coherent structural sheaves (in the sense of Faltings), we prove that the higher direct images of quasi-coherent and almost coherent modules are quasi-coherent and almost coherent. Our proof uses Noetherian approximation, inspired by Kiehl's proof of the pseudo-coherence of higher direct images. Our result allows us to extend Abbes-Gros' proof of Faltings' main $p$-adic comparison theorem in the relative case for projective log-smooth morphisms of schemes to proper ones, and thus also their construction of the relative Hodge-Tate spectral sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_01797 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Almost Coherence of Higher Direct Images He, Tongmu Algebraic Geometry Commutative Algebra 14F06 (primary), 13D02, 14F30 For a flat proper morphism of finite presentation between schemes with almost coherent structural sheaves (in the sense of Faltings), we prove that the higher direct images of quasi-coherent and almost coherent modules are quasi-coherent and almost coherent. Our proof uses Noetherian approximation, inspired by Kiehl's proof of the pseudo-coherence of higher direct images. Our result allows us to extend Abbes-Gros' proof of Faltings' main $p$-adic comparison theorem in the relative case for projective log-smooth morphisms of schemes to proper ones, and thus also their construction of the relative Hodge-Tate spectral sequence. |
| title | Almost Coherence of Higher Direct Images |
| topic | Algebraic Geometry Commutative Algebra 14F06 (primary), 13D02, 14F30 |
| url | https://arxiv.org/abs/2212.01797 |