Rational torsion points on Jacobians of modular curves
نویسندگان
چکیده
منابع مشابه
Rational points on Jacobians of hyperelliptic curves
We describe how to prove the Mordell-Weil theorem for Jacobians of hyperelliptic curves over Q and how to compute the rank and generators for the Mordell-Weil group.
متن کاملTorsion Points on Modular Curves
Let N ≥ 23 be a prime number. In this paper, we prove a conjecture of Coleman, Kaskel, and Ribet about the Q-valued points of the modular curve X0(N) which map to torsion points on J0(N) via the cuspidal embedding. We give some generalizations to other modular curves, and to noncuspidal embeddings of X0(N) into J0(N).
متن کاملTorsion points on modular curves and Galois Theory
In contrast to the geometric theory, where the different kinds of number pairs (x, y) that can occur as solutions are viewed as homogeneous, the arithmetic b g gggj b b bbstudy classifies more carefully the structure of solutions of specific type. That is, one tries to understand the solutions to the equation (*) where (x, y) are constrained to lie in some arithmetically defined set. One common...
متن کاملTorsion Points on Curves
EXAMPLES. (i) The multiplicative group A = Gm is the algebraic group whose points over a field are the nonzero elements of the field. Then for any field K, Tor Gm(K) are the roots of unity contained in K. (ii) A = Gm×Gm then Tor(A) = Tor(Gm)×Tor(Gm) = {(x, y) : x, y ∈ K are roots of unity}. (iii) Let A be an elliptic curve. Over the complex numbers we can uniformize A as A = C/L where L is a la...
متن کاملAlmost Rational Torsion Points on Semistable Elliptic Curves
If P is an algebraic point on a commutative group scheme A/K, then P is almost rational if no two non-trivial Galois conjugates σP , τP of P have sum equal to 2P . In this paper, we classify almost rational torsion points on semistable elliptic curves over Q. 1 Definitions and Results Let X be an algebraic curve of genus greater than one. Let J(X) be the Jacobian variety of X, and embed X in J(...
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: Acta Arithmetica
سال: 2015
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa8140-12-2015