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- W4366564133 abstract "Let $K$ be a number field and $ellgeq 5$ be a prime number. Mazur and Rubin introduced the notion of diophantine stability for a variety $X_{/K}$ at a prime $ell$. Under the hypothesis that all elliptic curves $E_{/mathbb{Q}}$ have finite Tate-Shafarevich group, we show that there is a positive density set of elliptic curves $E_{/mathbb{Q}}$ of rank $1$, such that $E_{/K}$ is diophantine stable at $ell$. This result has implications to Hilbert's tenth problem for number rings." @default.
- W4366564133 created "2023-04-22" @default.
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- W4366564133 date "2023-04-19" @default.
- W4366564133 modified "2023-09-26" @default.
- W4366564133 title "Diophantine stability for elliptic curves on average" @default.
- W4366564133 doi "https://doi.org/10.48550/arxiv.2304.09742" @default.
- W4366564133 hasPublicationYear "2023" @default.
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