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

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

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Plenty <strong>of</strong> Nonsquare Sha!<br />

• Theorem (<strong>Stein</strong>): For every prime<br />

p < 25000 there is an abelian variety<br />

A over Q such that<br />

• Conjecture (<strong>Stein</strong>): Same statement <strong>for</strong> all p.

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