Sur une conjecture de Schinzel
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912443614101504 |
|---|---|
| author | Amoroso, F. Andriamandratomanana, N. H. Simon, D. |
| author_facet | Amoroso, F. Andriamandratomanana, N. H. Simon, D. |
| contents | We give a new proof of a conjecture of Schinzel on the intersection of a subvariety of codimension at least 2 in a power of the multiplicative group with a torus of dimension 1. The proof rests on a geometric Bézout's theorem of P. Philippon and on lower bounds for the height of the first author, S. David and E. Viada. It gives for the first time an explicit result, depending on the height and degree of the variety. It is inspired on a similar statement on products of elliptic curves, by S. Checcoli, F. Veneziano and E. Viada. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10549 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sur une conjecture de Schinzel Amoroso, F. Andriamandratomanana, N. H. Simon, D. Number Theory We give a new proof of a conjecture of Schinzel on the intersection of a subvariety of codimension at least 2 in a power of the multiplicative group with a torus of dimension 1. The proof rests on a geometric Bézout's theorem of P. Philippon and on lower bounds for the height of the first author, S. David and E. Viada. It gives for the first time an explicit result, depending on the height and degree of the variety. It is inspired on a similar statement on products of elliptic curves, by S. Checcoli, F. Veneziano and E. Viada. |
| title | Sur une conjecture de Schinzel |
| topic | Number Theory |
| url | https://arxiv.org/abs/2502.10549 |