Some Obstructions to Solvable Points on Higher Genus Curves
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912640607977472 |
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| author | Rawson, James |
| author_facet | Rawson, James |
| contents | It is known that for a curve defined over $\mathbb{Q}$ of genus $g \leq 4$, there exists a point on the curve defined over a solvable extension of $\mathbb{Q}$. We relate points on curves of genus $g \geq 5$ over solvable extensions to the Bombieri-Lang conjecture. Specifically, we show that varieties parametrising points defined over extensions with a fixed solvable Galois group are of general type. Moreover, we show the existence of certain subvarieties in these varieties imply the existence of solvable morphisms from the curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_10367 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Some Obstructions to Solvable Points on Higher Genus Curves Rawson, James Number Theory 11G30, 11G35, 14G05 It is known that for a curve defined over $\mathbb{Q}$ of genus $g \leq 4$, there exists a point on the curve defined over a solvable extension of $\mathbb{Q}$. We relate points on curves of genus $g \geq 5$ over solvable extensions to the Bombieri-Lang conjecture. Specifically, we show that varieties parametrising points defined over extensions with a fixed solvable Galois group are of general type. Moreover, we show the existence of certain subvarieties in these varieties imply the existence of solvable morphisms from the curve. |
| title | Some Obstructions to Solvable Points on Higher Genus Curves |
| topic | Number Theory 11G30, 11G35, 14G05 |
| url | https://arxiv.org/abs/2211.10367 |