Independence of rational points on twists of a given curve
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Publication:5395480
DOI10.1112/S0010437X06002168zbMATH Open1128.11033arXivmath/0603557MaRDI QIDQ5395480
Author name not available (Why is that?)
Publication date: 31 October 2006
Published in: (Search for Journal in Brave)
Abstract: In this paper, we study bounds for the number of rational points on twists C' of a fixed curve C over a number field K, under the condition that the group of 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'(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 K_v, where v is a place of bad reduction for C'.
Full work available at URL: https://arxiv.org/abs/math/0603557
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