نتایج جستجو برای: weil rank
تعداد نتایج: 75769 فیلتر نتایج به سال:
In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions on an elliptic curve so that it has twists of arbitrary 2-Selmer rank, and we give lower bounds for the number of twists (with bounded conductor) that have a given 2-Selmer rank. As a consequence, under appropriate hypotheses we can find m...
Let K be a number field and A an abelian variety over K. The K-rational points of A are known to constitute a finitely generated abelian group (Mordell-Weil theorem). The problem studied in this paper is to find an explicit upper bound for the rank r of its free part in terms of other invariants of A/K. This is achieved by a close inspection of the classical proof of the so-called ‘weak Mordell...
We will give an upper bound of Mordell-Weil rank r for relatively minimal brations of curves of genus g 1 on rational surfaces. Under the assumption that a bration is not locally trivial, we have r 4g+4. Moreover the maximal case (r = 4g + 4) will be studied in detail. We determine the structure of such brations and also the structure of their Mordell-Weil lattices introduced by Shioda.
Shioda described in his article [6] a method to compute the Lefschetz number of a Delsarte surface. In one of his examples he uses this method to compute the rank of an elliptic curve over kptq. In this article we find all elliptic curves over kptq for which his method is applicable. For these curves we also compute the maximal Mordell-Weil rank.
We determine all complex K3 surfaces with Picard rank 20 over Q. Here the NéronSeveri group has rank 20 and is generated by divisors which are defined over Q. Our proof uses modularity, the Artin-Tate conjecture and class group theory. With different techniques, the result has been established by Elkies to show that Mordell-Weil rank 18 over Q is impossible for an elliptic K3 surface. We also a...
Faltings' theorem states that curves of genus g > 2 have finitely many rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one obtains an upper bound on the upper bound on the number of rational points [Szp85], XI, §2, but this bound is too large to be used in any reasonable sense. In 1985, Coleman showed [Col85] that Chabauty's method, which works when the Mordell-Weil ...
We determine all complex K3 surfaces with Picard rank 20 over Q. Here the NéronSeveri group has rank 20 and is generated by divisors which are defined over Q. Our proof uses modularity, the Artin-Tate conjecture and class group theory. With different techniques, the result has been established by Elkies to show that Mordell-Weil rank 18 over Q is impossible for an elliptic K3 surface. We also a...
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