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- W3092867307 abstract "We explore a number of problems related to the quadratic Chabauty method for determining integral points on hyperbolic curves. We remove the assumption of semistability in the description of the quadratic Chabauty sets $mathcal{X}(mathbb{Z}_p)_2$ containing the integral points $mathcal{X}(mathbb{Z})$ of an elliptic curve of rank at most $1$. Motivated by a conjecture of Kim, we then investigate theoretically and computationally the set-theoretic difference $mathcal{X}(mathbb{Z}_p)_2setminus mathcal{X}(mathbb{Z})$. We also consider some algorithmic questions arising from Balakrishnan--Dogra's explicit quadratic Chabauty for the rational points of a genus-two bielliptic curve. As an example, we provide a new solution to a problem of Diophantus which was first solved by Wetherell. Computationally, the main difference from the previous approach to quadratic Chabauty is the use of the $p$-adic sigma function in place of a double Coleman integral." @default.
- W3092867307 created "2020-10-22" @default.
- W3092867307 creator A5089066322 @default.
- W3092867307 date "2020-10-13" @default.
- W3092867307 modified "2023-09-25" @default.
- W3092867307 title "Quadratic Chabauty for (bi)elliptic curves and Kim’s conjecture" @default.
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- W3092867307 doi "https://doi.org/10.2140/ant.2020.14.2369" @default.
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