A motivic circle method
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866918006180806656 |
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| author | Bilu, Margaret Browning, Tim |
| author_facet | Bilu, Margaret Browning, Tim |
| contents | The circle method has been successfully used over the last century to study rational points on hypersurfaces. More recently, a version of the method over function fields, combined with spreading out techniques, has led to a range of results about moduli spaces of rational curves on hypersurfaces. In this paper a version of the circle method is implemented in the setting of the Grothendieck ring of varieties. This allows us to approximate the classes of these moduli spaces directly, without relying on point counting, and leads to a deeper understanding of their geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_09645 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A motivic circle method Bilu, Margaret Browning, Tim Algebraic Geometry Number Theory 14H10 (11D72, 11P55, 14E18) The circle method has been successfully used over the last century to study rational points on hypersurfaces. More recently, a version of the method over function fields, combined with spreading out techniques, has led to a range of results about moduli spaces of rational curves on hypersurfaces. In this paper a version of the circle method is implemented in the setting of the Grothendieck ring of varieties. This allows us to approximate the classes of these moduli spaces directly, without relying on point counting, and leads to a deeper understanding of their geometry. |
| title | A motivic circle method |
| topic | Algebraic Geometry Number Theory 14H10 (11D72, 11P55, 14E18) |
| url | https://arxiv.org/abs/2304.09645 |