QCI

Quadratic Chabauty and rational points. I: p-adic heights. 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 ℚ or a quadratic number field. We accomplish this by studying the role of p-adic heights in explicit non-abelian Chabauty.

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References in zbMATH (referenced in 9 articles , 1 standard article )

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  1. Cremona, John E.; Freitas, Nuno: Global methods for the symplectic type of congruences between elliptic curves (2022)
  2. Hashimoto, Sachi; Spelier, Pim: A geometric linear Chabauty comparison theorem (2022)
  3. Balakrishnan, Jennifer S.; Besser, Amnon; Bianchi, Francesca; Müller, J. Steffen: Explicit quadratic Chabauty over number fields (2021)
  4. Balakrishnan, Jennifer S.; Dogra, Netan: Quadratic Chabauty and rational points. II: Generalised height functions on Selmer varieties (2021)
  5. Box, Josha: Quadratic points on modular curves with infinite Mordell-Weil group (2021)
  6. Dogra, Netan; Le Fourn, Samuel: Quadratic Chabauty for modular curves and modular forms of rank one (2021)
  7. Beacom, Jamie: Computation of the unipotent Albanese map on elliptic and hyperelliptic curves (2020)
  8. Stoll, Michael: Diagonal genus 5 curves, elliptic curves over (\mathbbQ(t)), and rational Diophantine quintuples (2019)
  9. Balakrishnan, Jennifer S.; Dogra, Netan: Quadratic Chabauty and rational points. I: (p)-adic heights (2018)