Hasse principle for intersections of two quadrics via Kummer surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913442440413184 |
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| author | Morgan, Adam Skorobogatov, Alexei N. |
| author_facet | Morgan, Adam Skorobogatov, Alexei N. |
| contents | We prove new cases of the Hasse principle for Kummer surfaces constructed from 2-coverings of Jacobians of genus 2 curves, assuming finiteness of relevant Tate--Shafarevich groups. Under the same assumption, we deduce the Hasse principle for quartic del Pezzo surfaces with trivial Brauer group and irreducible or completely split characteristic polynomial, hence the Hasse principle for smooth complete intersections of two quadrics in the projective space of dimension at least 5. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16459 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hasse principle for intersections of two quadrics via Kummer surfaces Morgan, Adam Skorobogatov, Alexei N. Number Theory 14G12, 11D72 We prove new cases of the Hasse principle for Kummer surfaces constructed from 2-coverings of Jacobians of genus 2 curves, assuming finiteness of relevant Tate--Shafarevich groups. Under the same assumption, we deduce the Hasse principle for quartic del Pezzo surfaces with trivial Brauer group and irreducible or completely split characteristic polynomial, hence the Hasse principle for smooth complete intersections of two quadrics in the projective space of dimension at least 5. |
| title | Hasse principle for intersections of two quadrics via Kummer surfaces |
| topic | Number Theory 14G12, 11D72 |
| url | https://arxiv.org/abs/2407.16459 |