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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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The <strong>Shafarevich</strong>-<strong>Tate</strong><br />

Group <strong>of</strong> A f<br />

Sha is a subgroup <strong>of</strong> the first Galois cohomology<br />

<strong>of</strong> A f that measures failure <strong>of</strong> “local to global”:<br />

Example:<br />

Conjecture (<strong>Shafarevich</strong>-<strong>Tate</strong>):<br />

is finite.

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