About: Glossary of arithmetic and diophantine geometry

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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. Arithmetic geometry can be more generally defined as the study of schemes of finite type over the spectrum of the ring of integers. Arithmetic geometry has also been defined as the application of the techniques of algebraic geometry to problems in number theory.

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rdfs:label	Glossary of arithmetic and diophantine geometry (en)
rdfs:comment	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. Arithmetic geometry can be more generally defined as the study of schemes of finite type over the spectrum of the ring of integers. Arithmetic geometry has also been defined as the application of the techniques of algebraic geometry to problems in number theory. (en)
dcterms:subject	Glossaries of mathematics Diophantine geometry Algebraic geometry
Wikipage page ID	3141761 (xsd:integer)
Wikipage revision ID	1115935443 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Prime field Prime ideal Projective space Sato–Tate conjecture Motive (algebraic geometry) Mordell conjecture Mordellic variety Mordell–Lang conjecture Mordell–Weil theorem Jun-ichi Igusa Principal homogeneous space C. C. Tsen Non-Archimedean field Non-singular Normal variety Bernard Dwork Bernoulli number Birch and Swinnerton-Dyer conjecture David Masser Denominator Desingularisation Algebraic K-theory Algebraic cycle Algebraic differential equation Algebraic function Algebraic torus Algebraically closed field Arakelov theory Hodge conjecture John Tate (mathematician) Joseph Oesterlé Paul Vojta Richard Taylor (mathematician) Riemann hypothesis Ring of integers Cubic form Uniform boundedness conjecture for rational points Uniformity conjecture Valuation (algebra) Inverse Galois problem Iwasawa theory Jacobi sum Jacobian variety Elliptic curves L-function P-adic analysis Néron model Complex number Complex plane Mathematical logic Mathematics S-unit equation Chevalley–Warning theorem Elliptic surface Geometric class field theory Nevanlinna invariant Nevanlinna theory Semistable abelian variety Coates–Wiles theorem Elliptic curve Enrico Bombieri Generating function Geometric genus Gerd Faltings Goppa code Green's function Modular arithmetic Conjecture Crystalline cohomology Thin set (Serre) Thoralf Skolem Glossaries of mathematics Projective varieties Roots of unity Andrew Wiles André Weil Arakelov divisor Arithmetic genus Arithmetic geometry Arithmetic of abelian varieties Arithmetic topology Local zeta-function Singular curve Singularity theory Stickelberger's theorem Complex multiplication Zariski closure Zariski tangent space Étale cohomology Fubini–Study metric Functional equation (L-function) Ideal class group

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