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31 Aug 2011 Counterexamples to the Hasse principle. The counterexamples considered here extend the classical counterexample of 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.
show, by elementary means, that X has no Q(v?13)-rational divisor classes X is a counterexample to the Hasse principle, that is, X has no k-rational point.
I don't really know what you mean when you ask "Why is that a curve?". The question can be taken to mean either "I don't know what an
Among the first counterexamples to the Hasse principle were curves of genus 1 . the conic has equation y2 = b2, hence is a pair of lines (defined over K(. v.
existence of Q-points on a projective variety defined over Q given the existence of Qp-points for all p (including gives a counterexample to the Hasse Principle.
In this article we develop counterexamples to the Hasse principle using only . As a consequence, the problem of determining if a conic, defined over Q, has a
Counterexamples to the Hasse principle. Martin Bright. 16 April 2008. 1 The Hasse principle. If a polynomial equation defined over the rational numbers has no rational solutions, it can sometimes be very easy to prove this.
algebraic varieties defined over k is said to satisfy the Hasse principle if for Then X/Q is a counter-example to the Hasse principle if c is an odd rational.
In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, A counterexample by Ernst S. Selmer shows that the Hasse–Minkowski theorem The Hasse principle for algebraic groups states that if G is a simply-connected algebraic group defined over the global field k then the map from.
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