Concept information
Preferred term
Diophantine geometry
Definition(s)
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In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became clear for some mathematicians that methods of algebraic geometry are ideal tools to study these equations. Diophantine geometry is part of the broader field of arithmetic geometry.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Diophantine_geometry)
Broader concept(s)
Narrower concept(s)
- André-Oort conjecture
- Arakelov theory
- arithmetic of abelian varieties
- arithmetic surface
- Bogomolov conjecture
- Bombieri-Lang conjecture
- Chevalley-Warning theorem
- conductor of an abelian variety
- Diophantine equation
- Faltings's theorem
- Fermat curve
- field of definition
- height function
- height zeta function
- Igusa zeta function
- integer lattice
- local zeta function
- Manin conjecture
- Manin obstruction
- Mordellic variety
- Mordell-Weil group
- Mordell-Weil theorem
- Nevanlinna invariant
- principal homogeneous space
- Pythagorean quadruple
- quasi-algebraically closed field
- rational point
- semistable abelian variety
- Severi-Brauer variety
- Tate conjecture
- torsion conjecture
- Tsen rank
- Weil conjecture on Tamagawa numbers
- Zilber-Pink conjecture
In other languages
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French
URI
http://data.loterre.fr/ark:/67375/PSR-S0STN89F-1
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