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Author: William A. Stein
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* 45 minutes: general talk for number theorists
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* 30 minutes: specialist part 2
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Part I. General
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1. Define notion of visibility of H^1 and MW
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2. Prove everything visibility using Shapiro
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3. Visibility of Mordell-Weil
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-- E/Q yes; sketch proof
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-- conjecture: yes in general
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Part II. Sha
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4. Visibility of Sha
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5. Visualizing MW in Sha
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-- surprising nonsquare sha example
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-- conjecture: yes in general
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Part III. Modularity?
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6. Modularity of elements of Sha
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7. Visualizing MW in modular Sha
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