Number theory III: Diophantine geometry

Publication date: 18 September 1992

Published in: Encyclopaedia of Mathematical Sciences (Search for Journal in Brave)

zbMATH Keywords

intersection theory Number theory heights Heegner points Hasse principle Arakelov theory integral points Birch-Swinnerton-Dyer conjecture arithmetic algebraic geometry Diophantine geometry Mordell conjecture Mordell's conjecture diophantine approximations diophantine geometry arithmetic Nevanlinna type theory minimal isogenies between 1-motives Taniyama- Shimura-Weil conjecture

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Abelian varieties of dimension (> 1) (11G10) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Elliptic curves (14H52) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Measures of irrationality and of transcendence (11J82) Arithmetic ground fields for abelian varieties (14K15) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Arithmetic problems in algebraic geometry; Diophantine geometry (14Gxx) Global ground fields in algebraic geometry (14G25) Diophantine equations (11Dxx) Arithmetic algebraic geometry (Diophantine geometry) (11Gxx)

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