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Branch of algebraic geometry
mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered
Arithmetic_geometry
Theory in number theory
Anabelian geometry is a theory in arithmetic geometry which describes the way in which the algebraic fundamental group of a certain arithmetic variety X
Anabelian_geometry
Mathematics of varieties with integer coordinates
is part of the broader field of arithmetic geometry. Four theorems of fundamental importance in Diophantine geometry are: Mordell–Weil theorem Roth's
Diophantine_geometry
This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
Branch of mathematics
Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer.
Geometry
Liberal arts of arithmetic, geometry, music and astronomy
ways") is a pedogogical grouping of four historical mathematical arts—arithmetic, geometry, music, and astronomy— which was first taught in classical antiquity
Quadrivium
Natural number
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
1
techniques from algebraic geometry). It is named after Suren Arakelov. Arithmetic 1. Also known as elementary arithmetic, the methods and rules for
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
German mathematician (born 1987)
11 December 1987) is a German mathematician known for his work in arithmetic geometry. He has been a professor in the University of Bonn since 2012 and
Peter_Scholze
Venezuelan-American mathematician
Foundation from 2021-2026. Her research interests include arithmetic geometry and arithmetic dynamics in number theory. Salerno was born in Caracas in
Adriana_Salerno
Mathematics of Ancient Greece and the Mediterranean, 5th BC to 6th AD
since antiquity certain mathēmatá were granted special status: arithmetic, geometry, astronomy, and harmonics. These four mathēmatá, which appear listed
Ancient_Greek_mathematics
Mathematical theory
In mathematics, Arakelov theory (or Arakelov geometry) is an approach to Diophantine geometry, named for Suren Arakelov. It is used to study Diophantine
Arakelov_theory
Branch of mathematics
Real algebraic geometry is the study of the real algebraic varieties. Diophantine geometry and, more generally, arithmetic geometry is the study of algebraic
Algebraic_geometry
Mathematical theory by Shinichi Mochizuki
the 2000s, following his earlier work in arithmetic geometry. According to Mochizuki, it is "an arithmetic version of Teichmüller theory for number fields
Inter-universal Teichmüller theory
Inter-universal_Teichmüller_theory
General concept and operation in mathematics
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
Duality_(mathematics)
Japanese mathematician
mathematician working in number theory and arithmetic geometry. He is one of the main contributors to anabelian geometry. His contributions include his solution
Shinichi_Mochizuki
Bulgarian mathematician (born 1986)
The body of his work includes notable contributions to arithmetic geometry, Diophantine geometry, theory of modular forms and number theory. Dimitrov received
Vesselin_Dimitrov
South Korean mathematician (born 1963)
(Korean: 김민형) is a South Korean mathematician who specialises in arithmetic geometry and anabelian geometry. Kim received his PhD at Yale University in 1990 under
Minhyong_Kim
Field of mathematics
analogues of classical diophantine geometry in the setting of discrete dynamical systems, while local arithmetic dynamics, also called p-adic or nonarchimedean
Arithmetic_dynamics
Branch of elementary mathematics
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider
Arithmetic
Number
consequently dividing by 0 is generally considered to be undefined in arithmetic. As a numerical digit, 0 plays a crucial role in decimal notation: it
0
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
Arithmetic of abelian varieties
Arithmetic_of_abelian_varieties
Traditional academic course in Western higher education
of rhetoric, grammar, and logic, and the quadrivium of astronomy, arithmetic, geometry, and music. However, there are hundreds of modern disciplines of
Liberal_arts_education
Curves of genus > 1 over the rationals have only finitely many rational points
Faltings' theorem is a result in arithmetic geometry, according to which a non-singular algebraic curve of genus greater than 1 over the field Q {\displaystyle
Faltings'_theorem
American mathematician
American mathematician specializing in number theory, algebraic geometry, arithmetic geometry, and representation theory. She is an associate professor of
Wei_Ho
American mathematician (born 1937)
Fermat's Last Theorem in number theory, Mazur's torsion theorem in arithmetic geometry, the Mazur swindle in geometric topology, and the Mazur manifold
Barry_Mazur
MR 1807268. Kahn, Bruno. "Algebraic K-Theory, Algebraic Cycles and Arithmetic Geometry" (PDF). webusers.imj-prg.fr. Archived (PDF) from the original on
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Renaissance mathematics textbook
arithmetica, geometria, proportioni et proportionalita (Summary of arithmetic, geometry, proportions and proportionality) is a book on mathematics written
Summa_de_arithmetica
French mathematician
Cagnes-sur-Mer) is a French mathematician working in number theory and arithmetic geometry. Fargues was an invited speaker at the International Congress of
Laurent_Fargues
English-French mathematician
Francis Brown is a Franco-British mathematician who works on arithmetic geometry and quantum field theory. Brown studied at the University of Cambridge
Francis_Brown_(mathematician)
Tradition of pedagogy
comprised the trivium (grammar, rhetoric, and logic) and the quadrivium (arithmetic, geometry, music, and astronomy). This educational model aimed to cultivate
Classical_education
Concepts and results in arithmetic geometry and diophantine geometry can be found in Glossary of arithmetic and diophantine geometry. See also List of number
Glossary_of_number_theory
Particular mapping that projects a sphere onto a plane
make the polytope easier to visualize and understand. In elementary arithmetic geometry, stereographic projection from the unit circle provides a means to
Stereographic_projection
American mathematician
His research focuses on computational aspects of number theory and arithmetic geometry. He is known for his contributions to several projects involving
Andrew Sutherland (mathematician)
Andrew_Sutherland_(mathematician)
Scientific and philosophical encyclopedia by Avicenna
four parts: logic, natural sciences, mathematics (a quadrivium of arithmetic, geometry, astronomy), and metaphysics. It was influenced by ancient Greek
The_Book_of_Healing
American mathematician
generally, Balakrishnan specializes in algorithmic number theory and arithmetic geometry. She is a Clare Boothe Luce Professor at Boston University. Balakrishnan
Jennifer_Balakrishnan
Indian-American mathematician (born 1983)
Institute for Advanced Study and Princeton University and works in arithmetic geometry and commutative algebra. Bhatt graduated with a B.S. in Applied Mathematics
Bhargav_Bhatt_(mathematician)
Topics referred to by the same term
and Cinema The Seven Liberal Arts, being grammar, logic, rhetoric, arithmetic, geometry, music, and astronomy The Seven Arts, an artistic magazine Seven
Seven_arts
American mathematician (born 1955)
a professor of mathematics at Brown University working in arithmetic geometry, arithmetic dynamics, and cryptography. Joseph Silverman received an Sc
Joseph_H._Silverman
Canadian mathematician
Vatsal is a Canadian mathematician working in number theory and arithmetic geometry. Vatsal received his B.Sc. degree in 1992 from Stanford University
Vinayak_Vatsal
Study of algorithms for performing number theoretic computations
methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization
Computational_number_theory
Fedor Bogomolov, in arithmetic geometry about algebraic curves that generalizes the Manin–Mumford conjecture in arithmetic geometry. The conjecture was
Bogomolov_conjecture
Israeli-American mathematician
Israeli-American mathematician working in the fields of algebraic geometry and arithmetic geometry. As of 2019, he holds the title of L. Herbert Ballou University
Dan_Abramovich
Type of group in group theory
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
Arithmetic_group
Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for taxation, commerce, trade, and in astronomy, to record
History_of_mathematics
Invariant of algebraic varieties and of more general schemes
Conjecture and Motivic Cohomology with Finite Coefficients". The Arithmetic and Geometry of Algebraic Cycles. Section 5. doi:10.1007/978-94-011-4098-0_5
Motivic_cohomology
Mathematician
Yunqing Tang is a mathematician specialising in number theory and arithmetic geometry and an associate professor at the University of California, Berkeley
Yunqing_Tang
14th-century Byzantine mathematician and monk
monk who wrote a treatise named Easter Rule, along with books on arithmetic, geometry and astronomy. An Easter Rule, a treatise on Easter New Tables: An
Isaac_Argyros
Branch of pure mathematics
branch of mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties
Number_theory
Type of mathematical object
schemes that are not algebraic groups play a significant role in arithmetic geometry and algebraic topology, since they come up in contexts of Galois
Group_scheme
Venezuelan American mathematician
1950 Caracas, Venezuela) is an American mathematician working in arithmetic geometry and automorphic forms. He is a professor in the Department of Mathematics
Stephen_S._Kudla
Combinational digital circuit
In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers
Arithmetic_logic_unit
American mathematician
over multiple areas including algebraic geometry, algebraic topology, arithmetic geometry, and anabelian geometry. She is a professor of mathematics at
Kirsten_Wickelgren
Creative human and cultural expression
the quadrivium, a curriculum involving the "mathematical arts" of arithmetic, geometry, music, and astronomy. In modern academia, the arts can be grouped
The_arts
Group in arithmetic geometry
In arithmetic geometry, the Tate–Shafarevich group Ш(A/K) of an abelian variety A (or more generally a group scheme) defined over a number field K consists
Tate–Shafarevich_group
Indian mathematician (born 1961)
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
Dinesh_Thakur_(mathematician)
In arithmetic geometry, a Frobenioid is a category with some extra structure that generalizes the theory of line bundles on models of finite extensions
Frobenioid
American mathematician
Katz is a mathematician working in combinatorial algebraic geometry and arithmetic geometry. He is currently an associate professor in the Department of
Eric_Katz
Ancient Egyptian mathematical manuscript
ancient Egyptian mathematical papyrus containing several problems in arithmetic, geometry, and algebra. Golenishchev bought the papyrus in 1892 or 1893 in
Moscow_Mathematical_Papyrus
British mathematician
of pure mathematics at Imperial College London. He specialises in arithmetic geometry and the Langlands program. While attending the Royal Grammar School
Kevin_Buzzard
American mathematician (born 1966)
one of the principal investigators of the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation, a large multi-university collaboration
Noam_Elkies
Seven mathematical problems with a US$1 million prize for each solution
problems span a number of mathematical fields, namely algebraic geometry, arithmetic geometry, geometric topology, mathematical physics, number theory, partial
Millennium_Prize_Problems
American mathematician (born 1983)
University of Washington in Seattle. She works in arithmetic geometry, which is a blend of algebraic geometry and algebraic number theory. Viray received a
Bianca_Viray
conjecture Stickelberger's theorem Euler system p-adic L-function Arithmetic geometry Complex multiplication Abelian variety of CM-type Chowla–Selberg
List of algebraic number theory topics
List_of_algebraic_number_theory_topics
Field of knowledge
higher arithmetic) and geometry. Several other first-level areas have "geometry" in their names or are otherwise commonly considered part of geometry. Algebra
Mathematics
Historical development of geometry
relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic). Classic geometry was focused
History_of_geometry
American mathematician
at the University of Georgia who specializes in number theory and arithmetic geometry. He is one of the inventors of the Adleman–Pomerance–Rumely primality
Robert_Rumely
Mathematical concept
In arithmetic geometry, supersingular elliptic curves form a certain class of elliptic curves over a field of characteristic p > 0 {\displaystyle p>0}
Supersingular_elliptic_curve
Construct in mathematics
In arithmetic geometry, the Selmer group, named in honor of the work of Ernst Sejersted Selmer (1951) by John William Scott Cassels (1962), is a group
Selmer_group
Chinese mathematician (born 1981)
University working in number theory, arithmetic geometry, and automorphic forms. In particular, his work focuses on arithmetic intersection theory, algebraic
Xinyi_Yuan
Mathematical object studied in the field of algebraic geometry
Algebraic Geometry. Springer-Verlag. ISBN 0-387-90244-9. Hartshorne, Exercise I.2.9, p. 12 Liu, Qing (2010). Algebraic geometry and arithmetic curves (Reprinted ed
Algebraic_variety
First three liberal arts of traditional education
education in the liberal arts, which consists of arithmetic (numbers as abstract concepts), geometry (numbers in space), music (numbers in time), and
Trivium
French mathematician
Christophe Soulé (born 1951) is a French mathematician working in arithmetic geometry. Soulé started his studies in 1970 at École Normale Supérieure in
Christophe_Soulé
German mathematician (born 1954)
born 28 July 1954) is a German mathematician known for his work in arithmetic geometry. He was awarded the Fields Medal in 1986 for his proofs of the Mordell
Gerd_Faltings
French mathematician
Université Paris-Saclay in Orsay. He studies mainly number theory and arithmetic geometry. Prize of the French Academy of Sciences "Charles Louis de Saulces
Jean-Louis_Colliot-Thélène
Mathematics award
structures in higher dimensions." Xinwen Zhu – "For work in arithmetic algebraic geometry including applications to the theory of Shimura varieties and
Breakthrough Prize in Mathematics
Breakthrough_Prize_in_Mathematics
Dutch mathematician
at Columbia University. His research interests include arithmetic geometry and algebraic geometry. He maintains the Stacks Project. De Jong was born in
Aise_Johan_de_Jong
German mathematician (1938–2025)
1938 – 10 June 2025) was a German mathematician, specializing in arithmetic geometry and number theory. Harder studied mathematics and physics in Hamburg
Günter_Harder
American mathematician
Tangier) is an American mathematician, specializing in arithmetic geometry and algebraic geometry. Gillet received in 1974 his bachelor's degree from King's
Henri_Gillet
Symbolic and sacred meanings ascribed to certain geometric shapes
Sacred Geometry". Archived from the original on February 7, 2005. Catherine Goldstein, Norbert Schappacher, Joachim Schwermer, The shaping of arithmetic, p
Sacred_geometry
Mathematician
Elena Mantovan is a mathematician specializing in arithmetic geometry. Educated in Italy and the US, she works in the US as Taussky-Todd–Lonergan Professor
Elena_Mantovan
French mathematician (born 1959)
(born December 11, 1959) is a French mathematician, specializing in arithmetic geometry. André received his doctorate in 1984 from Pierre and Marie Curie
Yves_André
of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry, solid geometry, the shadow of the
Timeline_of_mathematics
Education from the Western world
comprised the trivium (grammar, rhetoric, and logic) and the quadrivium (arithmetic, geometry, music, and astronomy). This educational model aimed to cultivate
Western_education
Etymological encyclopedia compiled by Isidore of Seville
Quadrivium, the four subjects that supplemented the Trivium being arithmetic, geometry, music, and astronomy. He argues that there are infinitely many numbers
Etymologiae
Relates rational elliptic curves to modular forms
generalization of a modular form) to more general objects of arithmetic algebraic geometry, such as to every elliptic curve over a number field. Most cases
Modularity_theorem
German mathematician
the arithmetic geometry and representation theory research group at the University of Münster. Before that she was a professor working on arithmetic geometry
Eva_Viehmann
Mathematical algorithm
In arithmetic geometry, the Cox–Zucker machine is an algorithm introduced by David A. Cox and Steven Zucker for studying elliptic surfaces. It determines
Cox–Zucker_machine
Form of differential geometry
Sarnak in the case of arithmetic groups defined over Q, from their seminal 1994 paper. A bibliography for systoles in hyperbolic geometry currently numbers
Systolic_geometry
Russian mathematician (1942–2022)
1942 – 18 June 2022) was a Russian mathematician, specializing in arithmetic geometry. He is most well-known for his role in the proof of the Mordell conjecture
Aleksei_Parshin
Chinese-American mathematician (born 1962)
Chinese-American mathematician known for his work in number theory and arithmetic geometry. He is currently a Professor of Mathematics at Princeton University
Shou-Wu_Zhang
Norwegian international mathematics prize
award committee citing "the fundamental impact of her work on analysis, geometry and mathematical physics. The Bernt Michael Holmboe Memorial Prize was
Abel_Prize
Japanese mathematician (born 1952)
at the University of Chicago and specializes in number theory and arithmetic geometry. Kazuya Kato grew up in the prefecture of Wakayama in Japan. He attended
Kazuya_Kato
Literature of Sanskrit language
custom, grammar, politics, economics, medicine, astrology-astronomy, arithmetic, geometry, music, dance, dramatics, magic and divination, and sexuality. Literature
Sanskrit_literature
subject as it uses tools from algebraic number theory, arithmetic geometry, algebraic geometry, model theory, the theory of finite groups and of profinite
Field_arithmetic
Type of undergraduate qualification
study of many branches of learning such as grammar, logic, rhetoric, arithmetic, geometry, astronomy, and music. The study of liberal arts started during the
Bachelor_of_Arts
Chinese mathematician specializing in number theory
Professor at Peking University, specialising in number theory and arithmetic geometry. He is best known for his fundamental contributions to p-adic Hodge
Ruochuan_Liu
American mathematician (1925–2019)
fundamental contributions in algebraic number theory, arithmetic geometry, and related areas in algebraic geometry. He was awarded the Abel Prize in 2010. Tate
John_Tate_(mathematician)
French mathematician
Ullmo (born 25 June 1965) is a French mathematician, specialised in arithmetic geometry. Since 2013 he has served as director of the Institut des Hautes
Emmanuel_Ullmo
American mathematician
arithmetic geometry. He has authored or edited several books, including an exposition on Fermat's Last Theorem as well as a textbook about arithmetic
Glenn_H._Stevens
ARITHMETIC GEOMETRY
ARITHMETIC GEOMETRY
ARITHMETIC GEOMETRY
Boy/Male
Hindu, Indian, Sanskrit
Divine Rama
Girl/Female
Gaelic American Irish
Dark haired.
Boy/Male
Hindu, Indian, Marathi, Traditional
God Sivan
Girl/Female
Muslim
Close, Intimate, Good friend, Continuous
Girl/Female
Anglo Saxon American English Teutonic
Joyous.
Boy/Male
Hindu
Great victor of death
Boy/Male
Hindu
Lord Perumal, Good looking, Lion, Vishnus weapon
Girl/Female
Hindu, Indian, Tamil
Queen
Boy/Male
Latin American Greek
Ardent.
Girl/Female
Muslim
Plant known for its greenness
ARITHMETIC GEOMETRY
ARITHMETIC GEOMETRY
ARITHMETIC GEOMETRY
ARITHMETIC GEOMETRY
ARITHMETIC GEOMETRY
n.
A book containing the principles of this science.
v. i.
To perform the arithmetical operation of addition; as, he adds rapidly.
v. i.
To use figures in a mathematical process; to do sums in arithmetic.
n.
That part of arithmetic which treats of adding numbers.
v. t.
To subtract by arithmetical operation; to deduct.
a.
Of or pertaining to a unit or units; relating to unity; as, the unitary method in arithmetic.
a.
Of or pertaining to arithmetic; according to the rules or method of arithmetic.
n.
One skilled in arithmetic.
n.
The four "liberal arts," arithmetic, music, geometry, and astronomy; -- so called by the schoolmen. See Trivium.
adv.
Conformably to the principles or methods of arithmetic.
n.
A system of arithmetic, in which numbers are expressed in a scale of 60; logistic arithmetic.
a.
Having an assignable arithmetical or numerical value or meaning; not imaginary.
a.
Having equal differences; as, the terms of arithmetical progression are equidifferent.
n.
Arithmetical subtraction.
a.
Sexagesimal, or made on the scale of 60; as, logistic, or sexagesimal, arithmetic.
adv.
The arithmetical character 0; a cipher. See Cipher.
n.
The rule of three, in arithmetic, in which the three given terms, together with the one sought, are proportional.
n.
The science of numbers; the art of computation by figures.
v. t.
To subject to arithmetical division.
n.
Arithmetic.