Second isogeny descents and the Birch and Swinnerton-Dyer conjectural formula
نویسندگان
چکیده
منابع مشابه
The Birch and Swinnerton-Dyer conjectural formula Project description
This proposal falls broadly in the area of number theory and more specifically in arithmetic geometry. It is concerned with a part of the Birch and Swinnerton-Dyer (BSD) conjecture on elliptic curves and abelian varieties. A fundamental problem of number theory is: given a set of polynomial equations with rational coefficients, find all of its rational solutions and investigate their structure....
متن کاملThe Birch and Swinnerton-Dyer conjectural formula and visibility Project description
A fundamental problem of number theory is: given a set of polynomial equations with rational coefficients, find all of its rational solutions and investigate their structure. In many cases, the Birch and Swinnerton-Dyer conjecture (henceforth abbreviated BSD conjecture) predicts the existence of such solutions and describes some of their structure without actually finding the solutions. The imp...
متن کاملThe Birch-swinnerton-dyer Conjecture
We give a brief description of the Birch-Swinnerton-Dyer conjecture which is one of the seven Clay problems.
متن کاملThe Birch and Swinnerton-Dyer Conjecture
A polynomial relation f(x, y) = 0 in two variables defines a curve C. If the coefficients of the polynomial are rational numbers then one can ask for solutions of the equation f(x, y) = 0 with x, y ∈ Q, in other words for rational points on the curve. If we consider a non-singular projective model C of the curve then over C it is classified by its genus. Mordell conjectured, and in 1983 Falting...
متن کاملThe conjecture of Birch and Swinnerton-Dyer
This essay starts by first explaining, for elliptic curves defined over Q, the statement of the conjecture of Birch and Swinnerton-Dyer. Alongside, it contains a discussion of some results that have been proved in the direction of the conjecture, such as the theorem of Kolyvagin-Gross-Zagier and the weak parity theorem of Tim and Vladimir Dokchitser. The second, third and fourth part of the ess...
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: Journal of Algebra
سال: 2012
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2012.09.029