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Title of Journal: manuscripta math

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Abbravation: Manuscripta Mathematica

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Springer Berlin Heidelberg

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DOI

10.1002/fors.200790029

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1432-1785

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Extending Elliptic Curve Chabauty to higher genus

Authors: Michael Mourao
Publish Date: 2013/04/05
Volume: 143, Issue: 3-4, Pages: 355-377
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Abstract

We give a generalization of the method of “Elliptic Curve Chabauty” to higher genus curves and their Jacobians This method can sometimes be used in conjunction with covering techniques and a modified version of the Mordell–Weil sieve to provide a complete solution to the problem of determining the set of rational points on an algebraic curve Y We show how to apply these explicitly by using them to prove that the equation y 2 = x 3 + x 2 − 1 Φ11x has no rational solutions

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Other Papers In This Journal:
  1. A stability criterion for nonparametric minimal submanifolds
  2. Harmonic maps and asymptotic Teichmüller space
  3. On the backward uniqueness property for the heat equation in two-dimensional conical domains
  4. Minoration de la hauteur de Néron-Tate sur les surfaces abéliennes
  5. Stability of flows associated to gradient vector fields and convergence of iterated transport maps
  6. Willmore submanifolds of the Möbius space and a Bernstein-type theorem
  7. A positivity property of the Satake isomorphism
  8. Homological characterization of lean algebras
  9. Reduction of structure for torsors over semilocal rings
  10. Common divisors of elliptic divisibility sequences over function fields
  11. Finitistic dimensions of semiprimary rings
  12. The Sp 3 -grassmannian and duality for prime Fano threefolds of genus 9
  13. Existence and compactness for the $${\overline{\partial}}$$ -Neumann operator on q-convex domains
  14. The normalization constant of a certain invariant measure on GL n ()
  15. Tropical descendant Gromov–Witten invariants
  16. A Harnack inequality for the quasi-minima of scalar integral functionals with general growth conditions
  17. Cut loci and conjugate loci on Liouville surfaces
  18. A sphere theorem on locally conformally flat even-dimensional manifolds
  19. On the class numbers of certain Hilbert class fields
  20. The zeros of certain weakly holomorphic Drinfeld modular forms
  21. Icosahedral representations and elliptic curves
  22. On entire functions whose derivatives are¶integer-valued on geometric progressions
  23. Perversité et variation
  24. On linear combinations of special values of L -functions
  25. Irrationalité de certaines sommes de séries
  26. Deformations of Koszul Artin–Schelter Gorenstein algebras
  27. On positive definite hermitian forms
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