Rational Points in the Noether-Lefschetz Locus of Moduli Spaces of K3 Surfaces

Domenico Valloni
2024
Article

Résumé

We give a characterization of rational points lying on the Noether-Lefschetz locus of moduli spaces of K3 surfaces by studying their lifting properties under some natural coverings of the ambient space. We then prove that the Bombieri-Lang conjecture implies non-density statements for the rational points in the Noether-Lefschetz locus, as predicted by a conjecture of Shafarevich.

Source officielle

https://infoscience.epfl.ch/record/311396?ln=fr

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Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

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A set

R\subset \mathbb{N}

is called rational if it is well approximable by finite unions of arithmetic progressions, meaning that for every

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there exists a set

B=\bigcup _{i=1}^{r}a_{i}\mathbb{N}+b_{i}

, where $a_{1},\ldots ,a_ ...

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