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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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They Are Interesting!<br />

• Wiles et al.: Every elliptic curve<br />

over Q is modular, i.e., isogenous to an A f<br />

Consequence (Ribet): Fermat’s Last Theorem<br />

• Serre’s Conjecture: Every odd irreducible Galois representation<br />

occurs up to twist in the torsion points <strong>of</strong> some A f

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