Keyword

rational points

Description: Rational points are points on algebraic curves or other varieties whose coordinates belong to a specified rational number field, often the rational numbers.

Primary topic: Algebraic Geometry and Number Theory (77%)

Wikidata ID: wiki/Q3393476

OpenAlex ID: keywords/rational-points

The Arithmetic of Elliptic Curves

1986 · Joseph H. Silverman · Graduate texts in mathematics · 4,054

Fundamentals of Diophantine Geometry

1983 · Serge Lang · Springer eBooks · 984

Endlichkeitss�tze f�r abelsche Variet�ten �ber Zahlk�rpern

1983 · G. Faltings · Inventiones mathematicae · 959

The Arithmetic of Dynamical Systems

2007 · Joseph H. Silverman · Graduate texts in mathematics · 584

Heights in Diophantine geometry

2006 · Bombieri, Enrico, Gubler, Walter · Choice Reviews Online · 460

Rational Points on Elliptic Curves

2015 · Joseph H. Silverman, John T. Tate · Undergraduate texts in mathematics · 445

Rational points of abelian varieties with values in towers of number fields

1972 · Barry Mazur · Inventiones mathematicae · 424

Cubic Forms - Algebra, Geometry, Arithmetic

1986 · North-Holland mathematical library · 395

Diophantine Approximation on Abelian Varieties

1991 · Gerd Faltings · Annals of Mathematics · 365

Torsors and Rational Points

2001 · Alexei Skorobogatov · Cambridge University Press eBooks · 349

Rational Points on Elliptic Curves

1992 · Joseph H. Silverman, John Tate · Undergraduate texts in mathematics · 345

Rational points of bounded height on Fano varieties

1989 · Jens Franke, Yuri I. Manin, et al. · Inventiones mathematicae · 335

The arithmetic of elliptic curves

1974 · John T. Tate · Inventiones mathematicae · 291

Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2

1996 · J. W. S. Cassels, E. V. Flynn · Cambridge University Press eBooks · 281

The number of integral points on arcs and ovals

1989 · E. Bombieri, J. Pila · Duke Mathematical Journal · 270

Nonsingular plane cubic curves over finite fields

1987 · René Schoof · Journal of Combinatorial Theory Series A · 268

Universal Bounds on the Torsion of Elliptic Curves

1976 · Daniel Sion Kubert · Proceedings of the London Mathematical Society · 256

La $R$-équivalence sur les tores

1977 · Jean-Louis Colliot-Thélène, Jean-Jacques Sansuc · Annales Scientifiques de l École Normale Supérieure · 251

PDF

Hyperbolic and Diophantine analysis

1986 · Serge Lang · Bulletin of the American Mathematical Society · 240

PDF

Weierstrass Points and Curves Over Finite Fields

1986 · Karl-Otto Stöhr, José Felipe Voloch · Proceedings of the London Mathematical Society · 240

On the equation 𝑌²=𝑋(𝑋²+𝑝)

1984 · A. Bremner, J. W. S. Cassels · Mathematics of Computation · 234

PDF

Forms in many variables

1962 · B. J. Birch · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 232

The Mordell-Lang conjecture for function fields

1996 · Ehud Hrushovski · Journal of the American Mathematical Society · 223

PDF

The Density of Rational Points on Curves and Surfaces

2002 · D. R. Heath-Brown · Annals of Mathematics · 201

The Algorithmic Resolution of Diophantine Equations

1998 · Nigel P. Smart · Cambridge University Press eBooks · 195

Works count: 6,053

Citation count: 48,460