Chabauty methods using elliptic curves

By Nils Bruin. 2003

141 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/063221799b44584538854eb8aeda21d386d9eccc

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In Computational Mechanics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Torsion of rational elliptic curves over cubic fields and sporadic points on $X_1(n)$ (2012, background): “(9) 0 → E(L)[2] → E(L)[4] → (E(L)[4]/E(L)[2]) → H(1)(G,E(L)[2]) It is easy to compute that H1(G,E(L)[2]) = 0, and since E(L)[4]/E(L)[2] is a group of order 2, it follows that”
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].”
Elliptic curves over ℚ $\mathbb {Q}$ and 2-adic images of Galois (2014, background): “[8, 21]) and lies at the heart of the modular approach to Fermat’s last theorem (see [36], 5.”
Explicit Chabauty over number fields (2010, background): “The cases n = 7, 8, 9 are solved respectively in [Poonen et al. 2007; Bruin 2003; 2005].”
Generalized Fermat equations: A miscellany (2015, unknown): “(p, q, r) reference(s) (n, n, n), n ≥ 3 Wiles [68], Taylor-Wiles [66] (n, n, 2), n ≥ 4 Darmon-Merel [33], Poonen [57] (n, n, 3), n ≥ 3 Darmon-Merel [33], Poonen [57] (2n, 2n, 5), n ≥ 2 Bennett [1] (2, 4, n), n ≥ 4 Ellenberg [39], Bennett-Ellenberg-Ng [5], Bruin [15] (2, 6, n), n ≥ 3 Bennett-Chen [2]”
Periodic points, linearizing maps, and the dynamical Mordell–Lang problem (2008, methodology): “In particular, this should allow for the kinds of explicit computations that Flynn and Wetherell [FW99], Bruin [ Bru03 ], and others performed in the context of rational points on curves of genus greater than one.”
Integral points on hyperelliptic curves (2008, unknown): “N T ] 1 6 M ar 2 01 Y 2 ) = ( X 5 ) .”
Powers from Products of Consecutive Terms in Arithmetic Progression (2006, background): “If 5 | n+2d, {3, 6, 6, 9} leads to the conclusion that 3 | n, whereby [3, 4, 6], [3, 5, 9] and either [0, 4, 6] (if 7 | n + d) or [6, 8, 9] (in all other cases) provide the desired conclusion.”