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Elliptic Tales by Robert Gross, Avner Ash

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EPILOGUE

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Retrospect

We could have explained the Birch–Swinnerton-Dyer Conjecture in many fewer pages than we have used in this book. We wanted to move at a leisurely pace and give a bigger and more detailed picture. The BSD Conjecture has its natural context within the larger scope of modern algebraic geometry and number theory. Our story exemplifies how number theoretic problems that are very elementary to state can easily give rise to new and important mathematical ideas. Some of the methods we’ve explained were perhaps not obvious but after you get used them, they seem to be natural. As some philosopher said, habit is second nature.

Because ...

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