In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it...

sets, their study is a part of algebraic geometry that is called Diophantine geometry. The word Diophantine refers to the Hellenistic mathematician of...

be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the...

glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large...

theory (or Arakelov geometry) is an approach to Diophantine geometry, named for Suren Arakelov. It is used to study Diophantine equations in higher dimensions...

centered around Diophantine geometry, the study of rational points of algebraic varieties. In more abstract terms, arithmetic geometry can be defined as...

In the study of Diophantine geometry, the square lattice of points with integer coordinates is often referred to as the Diophantine plane. In mathematical...

Real algebraic geometry is the study of the real algebraic varieties. Diophantine geometry and, more generally, arithmetic geometry is the study of algebraic...

Walter Gubler (2006). Heights in Diophantine Geometry. Cambridge U. P. J. W. S. Cassels. An Introduction to the Geometry of Numbers. Springer Classics in...

complexity of mathematical objects. In Diophantine geometry, height functions quantify the size of solutions to Diophantine equations and are typically functions...

American mathematician, known for his work in number theory on Diophantine geometry and Diophantine approximation. In formulating Vojta's conjecture, he pointed...

number theory Diophantine geometry (Arakelov theory, Hodge–Arakelov theory) Arithmetic combinatorics (additive number theory) Arithmetic geometry (anabelian...

Diophantine equations are algebraic equations with integer coefficients for which integer solutions are sought. Diophantine geometry and Diophantine approximations...

Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land', and μέτρον (métron) 'a measure') is a branch of mathematics...

was a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic...

the geometric analogues of class field theory and diophantine geometry. Later he moved into diophantine approximation and transcendental number theory,...

In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus...

ISBN 978-0-08-096019-7. MR 0930670. Stillwell, John (1994). Elements of Algebra: Geometry, Numbers, Equations. Springer-Verlag. pp. xi, 1–181. ISBN 9783540942900...

known for his work in transcendental number theory, Diophantine approximation, and Diophantine geometry. With Joseph Oesterlé in 1985, Masser formulated...

mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...

the profane". The applications of model theory to algebraic and Diophantine geometry reflect this proximity to classical mathematics, as they often involve...

the fact that the space of the scheme is a point might suggest. In diophantine geometry the characteristic problems of the subject are those caused by the...

Italian mathematician, known for his work in analytic number theory, Diophantine geometry, complex analysis, and group theory. Bombieri is currently Professor...

Yuri Manin (1937–2023) – algebraic geometry and diophantine geometry Vladimir Arnold (1937–2010) – algebraic geometry Ernest Vinberg (1937–2020) J. H. Conway...

Alexander Grothendieck's approach to algebraic geometry, he moved into areas of diophantine geometry. Mazur's torsion theorem, which gives a complete...

theorem Diophantine geometry It is also closely related to the Manin–Mumford conjecture. Hindry, Marc; Silverman, Joseph H. (2000), Diophantine Geometry: An...

notion of a plane does not carry over.) It is now recognized that Euclidean geometry can be studied as a mathematical abstraction, but that the universe is...

In mathematics, specifically in transcendental number theory and Diophantine approximation, Siegel's lemma refers to bounds on the solutions of linear...

been in number theory, where it has a significant role in diophantine geometry and diophantine approximation. Some applications have required the development...

number theory, examining the interface of analytic number theory and Diophantine geometry. Browning is currently a Professor of number theory at the Institute...