Slope-determinant method, complex cellular structures and hypersurface coverings of regular rational points
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910731306270720 |
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| author | Chiu, Kenneth Chung Tak |
| author_facet | Chiu, Kenneth Chung Tak |
| contents | We use the determinant method of Bombieri-Pila and Heath-Brown and its Arakelov reformulation by Chen utilizing Bost's slope method to estimate the number of hypersurfaces required to cover the regular rational points with bounded Arakelov height on a projective variety. Using complex cellular structures introduced by Binyamini-Novikov, we replace the usual subpolynomial factor by a polylogarithmic factor in the estimation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05205 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Slope-determinant method, complex cellular structures and hypersurface coverings of regular rational points Chiu, Kenneth Chung Tak Number Theory Algebraic Geometry We use the determinant method of Bombieri-Pila and Heath-Brown and its Arakelov reformulation by Chen utilizing Bost's slope method to estimate the number of hypersurfaces required to cover the regular rational points with bounded Arakelov height on a projective variety. Using complex cellular structures introduced by Binyamini-Novikov, we replace the usual subpolynomial factor by a polylogarithmic factor in the estimation. |
| title | Slope-determinant method, complex cellular structures and hypersurface coverings of regular rational points |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2412.05205 |