Bounding the number of rational points on certain curves of high rank

By J. L. Wetherell. 2001

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Chabauty for symmetric powers of curves (2009, methodology): “(b) The second is that the Chabauty–Coleman strategy can often be adapted to compute C(K), as in [3], [4], [20], [22], [23], [36], [57].”
Integral points on hyperelliptic curves (2008, methodology): “(I) The first is Chabauty’s elegant method which in fact determines all rational points on C in many cases, provided the rank of the Mordell–Weil group of its Jacobian is strictly less than the genus g; see for example [22], [54].”
Explicit Chabauty over number fields (2010, methodology): “, and the number of rational points on twists of a given curve [56]. (b) The second is that the Chabauty–Coleman strategy can often be adapted to compute C(K), as in [6], [7], [32], [34], [35], [42], [59], and even the K-rational points on the symmetric powers of C [50]. This paper is inspired by a ”
Elliptic curves over ℚ $\mathbb {Q}$ and 2-adic images of Galois (2014, background): “Étale descent is a “going up” style technique, first studied in [CG89] and [Wet97] and developed as a full theory (especially the non-abelian case) in [Sko01].”
Thue equations and the method of Chabauty-Coleman (2002, result): “as we shall recall below, borrowing from [ Wet ].”