Elements of Order P in the Tate-šafarevič Group
نویسندگان
چکیده
منابع مشابه
Visualizing elements of order three in the Shafarevich-Tate group
1. Introduction. If we wish to write the equations of curves of genus 1 that give elements of the Shafarevich-Tate group of an elliptic curve over a number field K, a choice of ways is open to us. For example, if the element in question is of order 3 the curve of genus 1 corresponding to it occurs as a smooth plane cubic curve over K. In a recent article [C-M] we raised the question of when one...
متن کاملVisualizing Elements in the Shafarevich - Tate Group
As is well known, E(K) and X(E/K) are somehow linked in the sense that it is often easier to come by information about the Selmer group of E over K which is built out of both E(K) and X(E/K) than it is to get information about either of these groups separately. It occurred to us that, although these two groups (Mordell-Weil and X) are partners, so to speak, in the arithmetic analysis of the ell...
متن کاملVisible Elements of the Shafarevich-tate Group
We study a subgroup of the Shafarevich-Tate group of an abelian variety known as the visible subgroup. We explain the geometric intuition behind this subgroup, prove its finiteness and describe several techniques for exhibiting visible elements. Two important results are proved one what we call the visualization theorem, which asserts that every element of the Shafarevich-Tate group of an abeli...
متن کاملVisualizing elements of order 7 in the Tate–Shafarevich group of an elliptic curve
We study the elliptic curves in Cremona’s tables that are predicted by the Birch–SwinnertonDyer conjecture to have elements of order 7 in their Tate–Shafarevich group. We show that in many cases these elements are visible in an abelian surface or abelian 3-fold.
متن کاملOn invisible elements of the Tate-Shafarevich group
Mazur [8] has introduced the concept of visible elements in the Tate-Shafarevich group of optimal modular elliptic curves. We generalized the notion to arbitrary abelian subvarieties of abelian varieties and found, based on calculations that assume the BirchSwinnerton-Dyer conjecture, that there are elements of the Tate-Shafarevich group of certain sub-abelian varieties of J0(p) and J1(p) that ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 1970
ISSN: 0024-6093
DOI: 10.1112/blms/2.3.293