methods of algebraic geometry are ideal tools to study these equations. Diophantine geometry is part of the broader field of arithmetic geometry. Four theorems...

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

theory. For the number-theoretic applications, see glossary of arithmetic and Diophantine geometry. For simplicity, a reference to the base scheme is...

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

characteristic of a non-singular projective surface. Glossary of algebraic geometry Glossary of arithmetic and Diophantine geometry Glossary of commutative...

polynomials) Arakelov geometry also known as Arakelov theory Arakelov theory an approach to Diophantine geometry used to study Diophantine equations in higher...

unit quantity 150 min. Non-Diophantine arithmetics are arithmetic systems that violate traditional arithmetic intuitions and include equations like 1 +...

a glossary of concepts and results in number theory, a field of mathematics. Concepts and results in arithmetic geometry and diophantine geometry can...

theory topics List of number theory topics List of recreational number theory topics Glossary of arithmetic and Diophantine geometry List of prime numbers—not...

norm Bombieri–Vinogradov theorem Glossary of arithmetic and Diophantine geometry – Bombieri–Lang conjecture "Site of Caccioppoli Prize". Archived from...

properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics...

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It...

under linear equivalence. Glossary of arithmetic and Diophantine geometry Silverman, J.H. Advanced Topics in the Arithmetic of Elliptic Curves. Springer...

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

and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the...

curvature tensor List of differential geometry topics Glossary of Riemannian and metric geometry What follows is an incomplete list of the most classical...

introduction of theories with counter-intuitive properties (such as non-Euclidean geometries and Cantor's theory of infinite sets), and the discovery of apparent...

Arithmetic algebraic geometry (see Glossary of arithmetic and Diophantine geometry). Special values of L-functions. Conjectures of: Bloch Beilinson Deligne...

A finite geometry is any geometric system that has only a finite number of points. The familiar Euclidean geometry is not finite, because a Euclidean...

of Abelian groups", Fundamenta Mathematicae, 41 (2): 203–271, doi:10.4064/fm-41-2-203-271, MR 0072131. Ax, James; Kochen, Simon (1965), "Diophantine problems...

of the detailed definitions in the theory of schemes, see the glossary of scheme theory. The origins of algebraic geometry mostly lie in the study of...

higher-dimensional geometry only began in the 19th century, via the work of Arthur Cayley, William Rowan Hamilton, Ludwig Schläfli and Bernhard Riemann...

and examples came from number theory, geometry, analysis, and the solutions of algebraic equations. Most theories that are now recognized as parts of...

computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using...

college algebra, encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, whilst algebra...

Numerical algebraic geometry is a field of computational mathematics, particularly computational algebraic geometry, which uses methods from numerical...

solution is known. Arithmetic dynamics is a field that emerged in the 1990s that amalgamates two areas of mathematics, dynamical systems and number theory...

ISBN 0-8218-1095-2. MR 2104929. Zbl 1068.11023. Lang, Serge (1997). Survey of Diophantine Geometry. Springer-Verlag. ISBN 3-540-61223-8. Zbl 0869.11051. Lang, Serge...

subject is Lie sphere geometry. This article addresses his approach to transformation groups, which is one of the areas of mathematics, and was worked out by...

and provides basic definitions. A list of order-theoretic terms can be found in the order theory glossary. Orders are everywhere in mathematics and related...