Quadratic Chabauty and rational points, I: p-adic heights
By Jennifer S. Balakrishnan, Netan Dogra. Duke mathematical journal, 2016
73 citations recorded by the source corpus.
We give the first explicit examples beyond the Chabauty-Coleman method where Kim's nonabelian Chabauty program determines the set of rational points of a curve defined over $\mathbb{Q}$ or a quadratic number field. We accomplish this by studying the role of $p$-adic heights in explicit nonabelian Chabauty.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/b9a69d3e178f43361652e722cfd67707800ffb92
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In Applied Mathematics
In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- Quadratic Chabauty and Rational Points II: Generalised Height Functions on Selmer Varieties (2017, methodology): “The relation between the approach of this paper (which we refer to below as “QC2”) and previous related papers (“QC0” [5] and “QC1” [6]) may be summarised as follows: QC0 QC1 QC2 Scope (proof of finiteness of a superset) X(Z) for X/Q hyperelliptic with r = g X(K) for X/K with r < g + ρ(J)− 1, K = Q ”