Chow motives of genus one fibrations
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866918097715200000 |
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| author | Kawabe, Daiki |
| author_facet | Kawabe, Daiki |
| contents | Let $f: X \rightarrow C$ be a genus 1 fibration from a smooth projective surface, i.e. its generic fiber is a regular genus 1 curve. Let $j: J \rightarrow C$ be the Jacobian fibration of $f$. In this paper, we prove that the Chow motives of $X$ and $J$ are isomorphic. As an application, combined with our concomitant work on motives of quasi-elliptic fibrations, we prove Kimura finite-dimensionality for smooth projective surfaces not of general type with geometric genus 0. This generalizes Bloch-Kas-Lieberman's result to arbitrary characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_06162 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Chow motives of genus one fibrations Kawabe, Daiki Algebraic Geometry 14C15, 14J27, 14J28 Let $f: X \rightarrow C$ be a genus 1 fibration from a smooth projective surface, i.e. its generic fiber is a regular genus 1 curve. Let $j: J \rightarrow C$ be the Jacobian fibration of $f$. In this paper, we prove that the Chow motives of $X$ and $J$ are isomorphic. As an application, combined with our concomitant work on motives of quasi-elliptic fibrations, we prove Kimura finite-dimensionality for smooth projective surfaces not of general type with geometric genus 0. This generalizes Bloch-Kas-Lieberman's result to arbitrary characteristic. |
| title | Chow motives of genus one fibrations |
| topic | Algebraic Geometry 14C15, 14J27, 14J28 |
| url | https://arxiv.org/abs/2201.06162 |