Possibilities for Shafarevich-Tate Groups of Modular ... - William Stein

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Proof Sketch (1): Exact Sequence of Neron Models
Proof (2): Mazur’s Etale Cohomology Sha Theorem Mazur's Rational Points of Abelian Varieties with Values in Towers of Number Fields: In general this is not true, but our hypothesis on p and l are exactly strong enough to kill the relevant error terms.
Page 1 and 2: Possibilities for Shafarevich-Tate
Page 3 and 4: Abelian Varieties Abelian Variety:
Page 5 and 6: The Modular Jacobian J 1 (N) • J
Page 7 and 8: Extra structure • A is an abelian
Page 9 and 10: Weil Restriction of Scalars
Page 11 and 12: BSD Conjecture
Page 13 and 14: The Shafarevich-Tate Group
Page 15 and 16: The Dual Abelian Variety The dual o
Page 17 and 18: Cassels-Tate Pairing
Page 19 and 20: Michael Stoll’s Computation Durin
Page 21 and 22: Poonen-Stoll Theorem Theorem (Annal
Page 23 and 24: In 2002 I finally found Sha of orde
Page 25 and 26: Constructing Nonsquare Sha While at
Page 27: What is the Abelian Variety A? Let
Page 31 and 32: Proof (4): Apply Kato’s Finitenes
Page 33: Acknowledgements: Thank you for com

Possibilities for Shafarevich-Tate Groups of Modular ... - William Stein

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