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

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

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

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

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...

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

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

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

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

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...

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...

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

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

1938 – 10 June 2025) was a German mathematician, specializing in arithmetic geometry and number theory. Harder studied mathematics and physics in Hamburg...

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

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...

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}...

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...

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

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

since antiquity certain mathēmatá were granted special status: arithmetic, geometry, astronomy, and harmonics. These four mathēmatá, which appear listed...

comprised the trivium (grammar, rhetoric, and logic) and the quadrivium (arithmetic, geometry, music, and astronomy). This educational model aimed to cultivate...

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...

Fermat's Last Theorem in number theory, Mazur's torsion theorem in arithmetic geometry, the Mazur swindle in geometric topology, and the Mazur manifold...

arithmetica, geometria, proportioni et proportionalita (Summary of arithmetic, geometry, proportions and proportionality) is a book on mathematics written...

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

relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic). Classic geometry was focused...

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

schemes that are not algebraic groups play a significant role in arithmetic geometry and algebraic topology, since they come up in contexts of Galois...

Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the field...