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Links:
- Faltings theorem
- Mordell-Weil rank
- Mordell conjecture
- Mordell-Weil group
Mordell-Weil
Mazur’s theorem
Mordell-Weil
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unresolved links output
Mordell conjecture in Quick_Notes/2021-05-03, -Unsorted/Mordell-Weil, -Unsorted/arithmetic geometry MOC
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Tate-Shafarevich group
- Tags: - #todo/untagged - Refs: - #todo/add-references - Links: - Galois cohomology - Mordell-Weil
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Neron-Tate height
- Tags: - #pairing - Refs: - Height functions in number theory: https://people.math.harvard.edu/~sli/notes/math383_w18_notes.pdf#page=1 #resources/course-notes - Links: - Mordell-Weil - abelian variety - global field - elliptic curves
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Birch and Swinnerton-Dyer conjecture
- Tags: - #AG/elliptic-curves #open/conjectures - Refs: - Swinnerton-Dyer, Notes on elliptic curves. II - J. T. Tate, On the conjectures of Birch and Swinnerton-Dyer and a geometric analog. - Links: - elliptic curve - modularity - L function - motivic L function - Application: congruent number problem - Mazur’s theorem - Faltings theorem