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- W4301387287 abstract "Let $C$ be a smooth projective absolutely irreducible curve of genus $g geq 2$ over a number field $K$ of degree $d$, and denote its Jacobian by $J$. Denote the Mordell--Weil rank of $J(K)$ by $r$. We give an explicit and practical Chabauty-style criterion for showing that a given subset $cK subseteq C(K)$ is in fact equal to $C(K)$. This criterion is likely to be successful if $r leq d(g-1)$. We also show that the only solutions to the equation $x^2+y^3=z^{10}$ in coprime non-zero integers is $(x,y,z)=(pm 3, -2, pm 1)$. This is achieved by reducing the problem to the determination of $K$-rational points on several genus $2$ curves where $K=Q$ or $Q(sqrt[3]{2})$, and applying the method of this paper." @default.
- W4301387287 created "2022-10-05" @default.
- W4301387287 creator A5017561176 @default.
- W4301387287 date "2010-10-13" @default.
- W4301387287 modified "2023-09-25" @default.
- W4301387287 title "Explicit Chabauty over Number Fields" @default.
- W4301387287 doi "https://doi.org/10.48550/arxiv.1010.2603" @default.
- W4301387287 hasPublicationYear "2010" @default.
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