Obstructions to the Hasse principle in families
نویسندگان
چکیده
منابع مشابه
Counterexamples to the Hasse Principle
This article explains the Hasse principle and gives a self-contained development of certain counterexamples to this principle. The counterexamples considered are similar to the earliest counterexample discovered by Lind and Reichardt. This type of counterexample is important in the theory of elliptic curves: today they are interpreted as nontrivial elements in Tate– Shafarevich groups.
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Acknowledgements My greatest gratitude goes out to my supervisor Dr Daniel Chan. He helped me pick the topic for this thesis which turned out to be extremely interesting, helped me with the writing of this thesis and most importantly never refused to spend time with me to help me learn mathematics. I thank him deeply for this. I would to also like thank my high school maths teacher Ian Denton f...
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We generalize L. J. Mordell’s construction of cubic surfaces for which the Hasse principle fails.
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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 curv...
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ژورنال
عنوان ژورنال: manuscripta mathematica
سال: 2018
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-018-1009-0