Surjectivity and flatness over DVR's (after Moret-Bailly)
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910980177395712 |
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| author | Margaux, Benedictus |
| author_facet | Margaux, Benedictus |
| contents | We study morphisms of schemes $f : X \to S$ which are locally of finite type. We present conditions under which there exists a morphism $g : S'\to X$ of $S$--schemes such that $f \circ g $ is the canonical morphism $S'\to S$. Furthermore, we exhibit situations in which $f$ is flat surjective. Our results are mostly concerned with $S$ being the spectrum of a DVR. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01313 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Surjectivity and flatness over DVR's (after Moret-Bailly) Margaux, Benedictus Algebraic Geometry 14B25, 14E22 We study morphisms of schemes $f : X \to S$ which are locally of finite type. We present conditions under which there exists a morphism $g : S'\to X$ of $S$--schemes such that $f \circ g $ is the canonical morphism $S'\to S$. Furthermore, we exhibit situations in which $f$ is flat surjective. Our results are mostly concerned with $S$ being the spectrum of a DVR. |
| title | Surjectivity and flatness over DVR's (after Moret-Bailly) |
| topic | Algebraic Geometry 14B25, 14E22 |
| url | https://arxiv.org/abs/2506.01313 |