Counterexamples to the Hasse Principle: an Elementary Introduction
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چکیده
We give an elementary, self-contained exposition concerning counterexamples to the Hasse Principle. Our account, which uses only techniques from standard undergraduate courses in number theory and algebra, focusses on counterexamples similar to the original ones discovered by Lind and Reichardt. As discussed in an appendix, this type of counterexample is important in the theory of elliptic curves: today they are interpreted as nontrivial elements in the Tate-Shafarevich group.
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تاریخ انتشار 2005