An Explicit Algebraic Family of Genus-one Curves Violating the Hasse Principle
نویسنده
چکیده
One says that a variety X over Q violates the Hasse prin iple if X(Q v ) 6= ; for all ompletions Q v of Q (i.e., R and Q p for all primes p) but X(Q) = ;. Hasse proved that degree 2 hypersurfa es in P n satisfy the Hasse prin iple. In parti ular, if X is a genus 0 urve, then X satis es the Hasse prin iple, sin e the anti anoni al embedding of X is a oni in P 2 . Around 1940, Lind [Lin℄ and (independently, but shortly later) Rei hardt [Re℄ dis overed examples of genus 1 urves over Q that violate the Hasse prin iple, su h as the nonsingular
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