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Algebraic curves
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#	Item
431	CYCLES OF QUADRATIC POLYNOMIALS AND RATIONAL POINTS ON A GENUS 2 CURVE E. V. FLYNN, BJORN POONEN, AND EDWARD F. SCHAEFER Abstract. It has been conjectured that for N sufficiently large, there are no quadratic polynomials Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:36 Algebraic curves Field theory Analytic number theory Algebraic number theory Vector bundles Elliptic curve Algebraic number field Polynomial Ample line bundle Abstract algebra Algebra Mathematics
432	EXHIBITING SHA[2] ON HYPERELLIPTIC JACOBIANS N. BRUIN AND E.V. FLYNN Abstract. We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves, with an emphasis on the theory and prac Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:36 Niels Henrik Abel Abelian variety Elliptic curve Rational point Abelian group Hyperelliptic curve cryptography Imaginary hyperelliptic curve Abstract algebra Algebraic curves Algebra
433	Heegner points and Sylvester’s conjecture Samit Dasgupta and John Voight Abstract. We consider the classical Diophantine problem of writing positive integers n as the sum of two rational cubes, i.e. n = x3 + y 3 for x, Add to Reading List Source URL: people.ucsc.edu Language: English - Date: 2008-09-13 15:52:13 Algebraic number theory Elliptic curves Number theory Group theory Heegner point Modular form Birch and Swinnerton-Dyer conjecture Prime number Classical modular curve Abstract algebra Mathematics Analytic number theory
434	N -COVERS OF HYPERELLIPTIC CURVES N. BRUIN AND E.V. FLYNN Abstract. For a hyperelliptic curve C of genus g with a divisor class of order n = g + 1, we shall consider an associated covering collection of curves Dδ , each Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:36 Algebraic curves Hyperelliptic curve Elliptic curve Curve Symbol Algebraic number field Imaginary hyperelliptic curve Abstract algebra Geometry Mathematics
435	Journal de Théorie des Nombres de Bordeaux 00 (XXXX), 000–000 Non-trivial X Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2009-08-31 00:19:33 Field theory Group theory Elliptic curves Finite fields Abstract algebra Algebraic number theory Algebraic number field
436	Descent via Isogeny in Dimension 2 E. V. Flynn, Mathematical Institute, University of Oxford Abstract A technique of descent via 4-isogeny is developed on the Jacobian of a curve of genus 2 of the form: Y 2 = q1 (X)q2 (X Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:37 Analytic number theory Algebraic curves Elliptic curve Group theory Symbol Abelian variety Quadratic form Constructible universe Classical modular curve Algebraic geometry Abstract algebra Algebra
437	CANONICAL HEIGHTS ON THE JACOBIANS OF CURVES OF GENUS 2 AND THE INFINITE DESCENT E.V. FLYNN AND N.P. SMART Abstract. We give an algorithm to compute the canonical height on a Jacobian of a curve of genus 2. The computati Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:36 Algebraic number theory Analytic number theory Elliptic curve Group theory Kummer surface Algebraic number field P-adic number Prime number Abstract algebra Mathematics Field theory
438	THE HASSE PRINCIPLE AND THE BRAUER-MANIN OBSTRUCTION FOR CURVES E.V. FLYNN Abstract. We discuss a range of ways, extending existing methods, to demonstrate violations of the Hasse principle on curves. Of particular inter Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:36 Vector bundles Algebraic number theory Field theory Number theory Algebraic curves Elliptic curve Divisor Canonical bundle Hasse principle Abstract algebra Mathematics Algebraic geometry
439	Solving Diophantine Problems on Curves via Descent on the Jacobian E. V. Flynn, Mathematical Institute, University of Oxford §0. Introduction The theory of Jacobians of curves has largely been developed in a vacuum, wit Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:37 Abelian varieties Algebraic curves Elliptic curves Diophantine geometry Analytic number theory Mordell–Weil theorem Kummer surface Dual abelian variety Isogeny Abstract algebra Algebraic geometry Geometry
440	David R. Kohel School of Mathematics and Statistics University of Sydney, F07 NSW 2006 Australia DOB: 27 February 1966 Add to Reading List Source URL: echidna.maths.usyd.edu.au Language: English - Date: 2005-08-23 07:34:54 Elliptic curves Algebraic curves Analytic number theory Finite fields Computational number theory Magma computer algebra system Supersingular elliptic curve Heegner point Algorithmic Number Theory Symposium Abstract algebra Mathematics Geometry

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