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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2505.11348 |
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- Let $K$ be a number field and $S$ a finite set of primes of $K$. Scholl proved that there are only finitely many $K$-isomorphism classes of del Pezzo surfaces of any degree $1 \le d \le 9$ over $K$ with good reduction away from $S$. Let instead $K$ be the cyclotomic $\mathbb{Z}_5$-extension of $\mathbb{Q}$.In this paper, we show, for $d=3$, $4$, that there are infinitely many $\overline{\mathbb{Q}}$ isomorphism classes of del Pezzo surfaces, defined over $K$, with good reduction away from the unique prime above $5$.