Let be a smooth projective absolutely irreducible curve of genus over a number field , and denote its Jacobian by . Let be an integer and denote the -th symmetric power of by . In this paper we adapt the classic Chabauty–Coleman method to study the -rational points of . Suppose that has Mordell–Weil rank at most . We give an explicit and practical criterion for showing that a given subset is in fact equal to .
"Chabauty for symmetric powers of curves." Algebra Number Theory 3 (2) 209 - 236, 2009. https://doi.org/10.2140/ant.2009.3.209