Glossary of arithmetic and diophantine geometry information
This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality.
Diophantine geometry in general is the study of algebraic varieties V over fields K that are finitely generated over their prime fields—including as of special interest number fields and finite fields—and over local fields. Of those, only the complex numbers are algebraically closed; over any other K the existence of points of V with coordinates in K is something to be proved and studied as an extra topic, even knowing the geometry of V.
Arithmetic geometry can be more generally defined as the study of schemes of finite type over the spectrum of the ring of integers.[1] Arithmetic geometry has also been defined as the application of the techniques of algebraic geometry to problems in number theory.[2]
Contents:
Top
0–9
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
^Arithmetic geometry at the nLab
^Sutherland, Andrew V. (September 5, 2013). "Introduction to Arithmetic Geometry" (PDF). Retrieved 22 March 2019.
and 28 Related for: Glossary of arithmetic and diophantine geometry information
This is a glossaryofarithmeticanddiophantinegeometry in mathematics, areas growing out of the traditional study ofDiophantine equations to encompass...
methods of algebraic geometry are ideal tools to study these equations. Diophantinegeometry is part of the broader field ofarithmeticgeometry. Four theorems...
theory topics List of number theory topics List of recreational number theory topics GlossaryofarithmeticandDiophantinegeometry List of prime numbers—not...
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...
unit quantity 150 min. Non-Diophantinearithmetics are arithmetic systems that violate traditional arithmetic intuitions and include equations like 1 +...
algebraic geometry is the study of the real algebraic varieties. Diophantinegeometryand, more generally, arithmeticgeometry is the study of algebraic...
curvature tensor List of differential geometry topics Glossaryof Riemannian and metric geometry What follows is an incomplete list of the most classical...
polynomials) Arakelov geometry also known as Arakelov theory Arakelov theory an approach to Diophantinegeometry used to study Diophantine equations in higher...
Differential geometry is a mathematical discipline that studies the geometryof smooth shapes and smooth spaces, otherwise known as smooth manifolds. It...
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...
equivalence. GlossaryofarithmeticandDiophantinegeometry Arakelov theory Néron model Silverman, J.H. Advanced Topics in the Arithmeticof Elliptic Curves...
those ofarithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations...
Numerical algebraic geometry is a field of computational mathematics, particularly computational algebraic geometry, which uses methods from numerical...
higher-dimensional geometry only began in the 19th century, via the work of Arthur Cayley, William Rowan Hamilton, Ludwig Schläfli and Bernhard Riemann...
introduction of theories with counter-intuitive properties (such as non-Euclidean geometriesand Cantor's theory of infinite sets), and the discovery of apparent...
college algebra, encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, whilst algebra...
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...
McKean; Victor Moll (1999). Elliptic curves: function theory, geometryandarithmetic. Cambridge University Press. ISBN 0-521-65817-9. Ivan Niven; Herbert...
solution is known. Arithmetic dynamics is a field that emerged in the 1990s that amalgamates two areas of mathematics, dynamical systems and number theory...
and examples came from number theory, geometry, analysis, and the solutions of algebraic equations. Most theories that are now recognized as parts of...
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...
geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables 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...