mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered...

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

figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called...

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

(or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions...

quadrivium (plural: quadrivia) was a grouping of four subjects or arts—arithmetic, geometry, music, and astronomy—that formed a second curricular stage following...

Anabelian geometry is a theory in number theory which describes the way in which the algebraic fundamental group G of a certain arithmetic variety X, or...

recognized as elliptic curves; and has become a very substantial area of arithmetic geometry both in terms of results and conjectures. Most of these can be posed...

11 December 1987) is a German mathematician known for his work in arithmetic geometry. He has been a professor at the University of Bonn since 2012 and...

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

of rhetoric, grammar, and logic, and the quadrivium of astronomy, arithmetic, geometry, and music. Since the late 1990s, major universities have gradually...

analogues of classical diophantine geometry in the setting of discrete dynamical systems, while local arithmetic dynamics, also called p-adic or nonarchimedean...

Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider...

conjecture Stickelberger's theorem Euler system p-adic L-function Arithmetic geometry Complex multiplication Abelian variety of CM-type Chowla–Selberg...

for the action of certain arithmetic groups on the relevant symmetric spaces. The topic was related to Minkowski's geometry of numbers and the early development...

theorem is self-dual in this sense under the standard duality in projective geometry. In mathematical contexts, duality has numerous meanings. It has been described...

techniques from algebraic geometry). It is named after Suren Arakelov. Arithmetic 1.   Also known as elementary arithmetic, the methods and rules for...

higher arithmetic) and geometry. Several other first-level areas have "geometry" in their names or are otherwise commonly considered part of geometry. Algebra...

the 2000s, following his earlier work in arithmetic geometry. According to Mochizuki, it is "an arithmetic version of Teichmüller theory for number fields...

for 15 years a participant in-the NSF-funded Southwest Center for Arithmetic Geometry and the Arizona Winter School. He was elected as a member of the...

In mathematics, Arakelov theory (or Arakelov geometry) is an approach to Diophantine geometry, named for Suren Arakelov. It is used to study Diophantine...

Faltings's theorem is a result in arithmetic geometry, according to which a curve of genus greater than 1 over the field Q {\displaystyle \mathbb {Q}...

and Film The Seven Liberal Arts, being grammar, logic, rhetoric, arithmetic, geometry, music, and astronomy The Seven Arts, an artistic magazine Seven...

In arithmetic geometry, the Cox–Zucker machine is an algorithm created by David A. Cox and Steven Zucker. This algorithm determines whether a given set...

1088/0026-1394/31/6/013. Peano, Giuseppe (1889). Arithmetices principia, nova methodo exposita [The principles of arithmetic, presented by a new method]. An excerpt...

ancient Egyptian mathematical papyrus containing several problems in arithmetic, geometry, and algebra. Golenishchev bought the papyrus in 1892 or 1893 in...

methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization...

mathematician working in number theory and arithmetic geometry. He is one of the main contributors to anabelian geometry. His contributions include his solution...

(born December 7, 1943) is an American mathematician, working in arithmetic geometry, particularly on p-adic methods, monodromy and moduli problems, and...

In mathematics, the arithmetic genus of an algebraic variety is one of a few possible generalizations of the genus of an algebraic curve or Riemann surface...