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

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What Next? • Remove the hypothesis that p
Acknowledgements: Thank you <strong>for</strong> coming! Kevin Buzzard, Cristian Gonzalez, Barry Mazur, Bjorn Poonen, Ken Ribet, and Michael Stoll For more details including an accepted paper: http://modular.fas.harvard.edu/papers/nonsquaresha/.
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 and 28: What is the Abelian Variety A? Let
Page 29 and 30: Proof (2): Mazur’s Etale Cohomolo
Page 31: Proof (4): Apply Kato’s Finitenes

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

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