Thue equations and the method of Chabauty-Coleman

By Dino J. Lorenzini, T. Tucker. 2002

58 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/020390c04ce4b899e4087a64d9c0e25c356c01b1

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Explicit Chabauty over number fields (2010, methodology): “Coleman’s approach has been adapted to give bounds (assuming some reasonable conditions) for the number of solutions of Thue equations [Lorenzini and Tucker 2002], the number of rational points on Fermat curves [McCallum 1992; 1994], the number of points on curves of the form y2 = x5+ A [Stoll 2006b”
Linear series on metrized complexes of algebraic curves (2012, background): “Lorenzini and Tucker [32] (see also [35]) proved the same bound as Coleman without assuming that X has good reduction at p; in their bound, X̄(Fp) is replaced by X̄(Fp) where X is a proper regular model for X over Op and X̄sm is the smooth locus of the special fiber of X.”
Uniform bounds for the number of rational points on curves of small Mordell–Weil rank (2015, methodology): “Coleman’s method has been refined by many authors: these authors [36], [38], [39], [48] allow X to have bad reduction at p and improve the 2g 2 to 2r ; [41], [46] generalize to symmetric powers of curves; and a large body of work by many authors allow one to explicitly execute this method in Magma f”
Chabauty for symmetric powers of curves (2009, methodology): “Coleman’s approach has been adapted to give bounds (assuming some reasonable conditions) for the number of solutions of Thue equations [33], the number of rational points on Fermat’s curves [34], [35], the number of points on curves of the form y2 = x5 + A [52], and the number of rational points on…”
Degeneration of Linear Series from the Tropical Point of View and Applications (2015, background): “In [LT02], Lorenzini and Tucker (see also McCallum–Poonen [MP12]) generalized Theorem 11.”