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ALGEBRAIC CURVES WITH SMALL GENUS AND SHARP CHABAUTY-COLEMAN’S BOUND
Keywords:
Sharp curve, Jacobian, rank Mordell-Weil, Coleman bound.DOI:
https://doi.org/10.17654/0972555524022Abstract
The Chabauty-Coleman bound gives an upper bound of the set of rational points on an algebraic curve whose Mordell-Weil rank of its Jacobian is less than its genus. In this paper, we construct algebraic curves of small genus which meet this bound in a prime $p$ of good reduction.
Received: February 9, 2024
Revised: March 7, 2024
Accepted: March 29, 2024
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