An “anti-hasse Principle” for Prime Twists
نویسنده
چکیده
Given an algebraic curve C/Q having points everywhere locally and endowed with a suitable involution, we show that there exists a positive density family of prime quadratic twists of C violating the Hasse principle. The result applies in particular to wN -Atkin-Lehner twists of most modular curves X0(N) and to wp-Atkin-Lehner twists of certain Shimura curves XD+.
منابع مشابه
Curves over Global Fields Violating the Hasse Principle
We exhibit for each global field k an algebraic curve over k which violates the Hasse Principle. We can find such examples among Atkin-Lehner twists of certain elliptic modular curves and Drinfeld modular curves. Our main tool is a refinement of the “Twist Anti-Hasse Principle” (TAHP). We then use TAHP to construct further Hasse Principle violations, e.g. among curves over any number field of a...
متن کاملCongruences for critical values of higher derivatives of twisted Hasse-Weil L-functions
et E be an elliptic curve defined over a number field k and F a finite cyclic extension of k of p-power degree for an odd prime p. Under certain technical hypotheses, we describe a reinterpretation of the Equivariant Tamagawa Number Conjecture (‘ETNC’) for E, F/k and p as an explicit family of p-adic congruences involving values of derivatives of the Hasse-Weil L-functions of twists of E, norma...
متن کاملCertain K3 Surfaces Parametrized by the Fibonacci Sequence Violate the Hasse Principle
For a prime p ≡ 5 (mod 8) satisfying certain conditions, we show that there exist an infinitude of K3 surfaces parameterized by certain solutions to Pell’s equation X2 − pY 2 = 4 in the projective 5-space that are counterexamples to the Hasse principle explained by the Brauer-Manin obstruction. Further, these surfaces contain no zero-cycle of odd degree over Q. As an illustration for the main r...
متن کاملSelmer Groups of Quadratic Twists of Elliptic Curves
(1.1) E : y + a1xy + a3y = x + a2x + a4x+ a6 where a1, a2, a3, a4, a6 ∈ Z. Let N(E) denote the conductor of E, j(E) the j-invariant of E, and L(E, s) = ∑∞ n=1 a(n)n −s the Hasse-Weil L-function of E. If E is modular, then let FE(z) = ∑∞ n=1 aE(n)q n ∈ S2(N(E), χ1) be the associated weight 2 cusp form. Here χ1 denotes the trivial Dirichlet character. Throughout, D will denote a square-free integ...
متن کاملDiscrete Logarithms and Mordell-Weil Groups
Let Ep be an elliptic curve over a prime finite field Fp, p ≥ 5, and Pp, Qp ∈ Ep(Fp). The elliptic curve discrete logarithm problem, ECDLP, on Ep is to find mp ∈ Fp such that Qp = mpPp if Qp ∈ 〈Pp〉. We propose an algorithm to attack the ECDLP relying on a Hasse principle detecting linear dependence in Mordell-Weil groups of elliptic curves via a finite number of reductions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007