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- W3105935601 abstract "HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button. In this paper, we study bounds for the number of rational points on twists $C'$ of a fixed curve $C$ over a number field ${mathcal K}$, under the condition that the group of ${mathcal K}$-rational points on the Jacobian $J'$ of $C'$ has rank smaller than the genus of $C'$. The main result is that with some explicitly given finitely many possible exceptions, we have a bound of the form $2r + c$, where $r$ is the rank of $J'({mathcal K})$ and $c$ is a constant depending on $C$. For the proof, we use a refinement of the method of Chabauty–Coleman: the main new ingredient is to use it for an extension field of ${mathcal K}_v$, where $v$ is a place of bad reduction for $C'$." @default.
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- W3105935601 date "2006-09-01" @default.
- W3105935601 modified "2023-10-02" @default.
- W3105935601 title "Independence of rational points on twists of a given curve" @default.
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- W3105935601 doi "https://doi.org/10.1112/s0010437x06002168" @default.
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