A threefold violating a local-to-global principle for rationality
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912068431511552 |
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| author | Frei, Sarah Ji, Lena |
| author_facet | Frei, Sarah Ji, Lena |
| contents | In this note we construct an example of a smooth projective threefold that is irrational over $\mathbb Q$ but is rational at all places. Our example is a complete intersection of two quadrics in $\mathbb P^5$, and we show it has the desired rationality behavior by constructing an explicit element of order $4$ in the Tate--Shafarevich group of the Jacobian of an associated genus $2$ curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_09306 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A threefold violating a local-to-global principle for rationality Frei, Sarah Ji, Lena Algebraic Geometry Number Theory Primary: 14E08. Secondary: 14G12, 14J20, 11G30 In this note we construct an example of a smooth projective threefold that is irrational over $\mathbb Q$ but is rational at all places. Our example is a complete intersection of two quadrics in $\mathbb P^5$, and we show it has the desired rationality behavior by constructing an explicit element of order $4$ in the Tate--Shafarevich group of the Jacobian of an associated genus $2$ curve. |
| title | A threefold violating a local-to-global principle for rationality |
| topic | Algebraic Geometry Number Theory Primary: 14E08. Secondary: 14G12, 14J20, 11G30 |
| url | https://arxiv.org/abs/2304.09306 |