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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
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
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
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
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
Chinese mathematician
1989) is a Chinese mathematician specialising in number theory and arithmetic geometry. She is a professor of mathematics at the University of California
Yunqing_Tang
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
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
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
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
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
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
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
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
Bulgarian mathematician (born 1986)
Димитров) is a Bulgarian mathematician known for his work in arithmetic geometry, Diophantine geometry, modular forms and number theory. He is currently a professor
Vesselin_Dimitrov
Canadian mathematician (born 1988)
was awarded for "outstanding work in analytic number theory and arithmetic geometry, including breakthroughs on the André-Oort and Griffiths conjectures"
Jacob_Tsimerman
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
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
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
In mathematics, an arithmetic variety is the quotient space of a Hermitian symmetric space by an arithmetic subgroup of the associated algebraic Lie group
Arithmetic_variety
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
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
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
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
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
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
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
Fedor Bogomolov, in arithmetic geometry about algebraic curves that generalizes the Manin–Mumford conjecture in arithmetic geometry. The conjecture was
Bogomolov_conjecture
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)
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
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
Renaissance mathematics textbook
arithmetica, geometria, proportioni et proportionalita (Summary of arithmetic, geometry, proportions and proportionality) is a book on mathematics written
Summa_de_arithmetica
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)
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
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)
American mathematician
American mathematician specializing in number theory, algebraic geometry, arithmetic geometry, and representation theory. She is an associate professor of
Wei_Ho
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
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
German mathematician
working at Rikkyo University in Tokyo, Japan. He works in the field of arithmetic geometry, motivic cohomology and algebraic K-theory. From 1985 Geisser studied
Thomas_Geisser
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)
Mathematical conjecture
liftings and dense sets of CM points", in Fabrizio Catanese (ed.), Arithmetic Geometry, Cambridge: Cambridge University Press. Klingler, Bruno; Yafaev,
André–Oort_conjecture
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
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
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
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)
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
Russian mathematician
Moscow) is a Russian mathematician, specializing in algebraic and arithmetic geometry and its applications to mathematical physics. He is a professor at
Victor_Batyrev
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
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
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
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
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
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
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
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
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
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
Chinese professor of mathematics
University specializing in number theory, automorphic forms and arithmetic geometry. Liu graduated from Peking University with a Bachelor of Science
Yifeng_Liu
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
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
Japanese mathematician (1930–2019)
Princeton University who worked in number theory, automorphic forms, and arithmetic geometry. He was known for developing the theory of complex multiplication
Goro_Shimura
Tunisian-French mathematician (born 1970)
Hautes Études Scientifiques (IHÉS). He is known for his work in arithmetic geometry. Abbes was born on 24 May 1970 in Sfax, Tunisia. Abbes received a
Ahmed_Abbes
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
over multiple areas including algebraic geometry, algebraic topology, arithmetic geometry, and anabelian geometry. She is a professor of mathematics at
Kirsten_Wickelgren
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
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
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
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
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
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
Japanese mathematician (born 1952)
of Chicago, as a professor, and specializes in number theory and arithmetic geometry. He is a member of the American Academy of Arts and Sciences, elected
Kazuya_Kato
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
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
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
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
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
French mathematician
and a professor of mathematics at Sorbonne University who works in arithmetic geometry. Mézard studied at the École normale supérieure de Lyon from 1992
Ariane_Mézard
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
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
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
Dutch mathematician (1962–2022)
1962 – 16 January 2022) was a Dutch mathematician who worked in arithmetic geometry. He was a professor at University of Rennes 1 and Leiden University
Bas_Edixhoven
Mathematical theory for p-adic formal schemes
In mathematics, specifically arithmetic geometry, prismatic cohomology is a cohomology introduced by Bhargav Bhatt and Peter Scholze for p-adic formal
Prismatic_cohomology
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
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
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
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
American mathematician (born 1981)
specifically, her research centers on arithmetic statistics, with excursions into related questions in arithmetic geometry and probability theory.[citation
Melanie_Wood
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
Mathematics award
Vlad Vicol "In recognition of his ground-breaking work in arithmetic geometry and arithmetic aspects of automorphic forms." "In recognition of the profound
Clay_Research_Award
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
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
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
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
Academic and research institution
of grammar, rhetoric and dialectic or logic–and the quadrivium: arithmetic, geometry, music, and astronomy. The earliest universities were developed under
University
Area of mathematics
studying these analogies, coining the term arithmetic topology for this area of study. Arithmetic geometry Arithmetic dynamics Topological quantum field theory
Arithmetic_topology
French mathematician (1941–2020)
was a French mathematician known for his work in number theory, arithmetic geometry, and commutative algebra. He formulated Szpiro's conjecture and was
Lucien_Szpiro
German mathematician and theologian
mathematics, he had a duty to provide lectures, which he did in arithmetic and geometry in the summer, and trigonometry and astronomy in the winter. Apart
Johann_Friedrich_Schultz
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
French writer and humanist (died 1553)
and dialectic before moving on to the quadrivium, which dealt with arithmetic, geometry, music, and astronomy. In 1623, Jacques Bruneau de Tartifume wrote
François_Rabelais
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