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Torsion points on modular curves
 Invent. Math
, 1999
"... Abstract. Let N ≥ 23 be a prime number. In this paper, we prove a conjecture of Coleman, Kaskel, and Ribet about the Qvalued 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 em ..."
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Abstract. Let N ≥ 23 be a prime number. In this paper, we prove a conjecture of Coleman, Kaskel, and Ribet about the Qvalued 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
TORSION POINTS ON CURVES AND COMMON
, 2002
"... Abstract. We study the behavior of the greatest common divisor of a k − 1 and b k − 1, where a, b are fixed integers or polynomials, and k varies. In the integer case, we conjecture that when a and b are multiplicatively independent and in addition a−1 and b−1 are coprime, then a k −1 and b k −1 are ..."
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are coprime infinitely often. In the polynomial case, we prove a strong version of this conjecture. To do this we use a result of Lang’s on the finiteness of torsion points on algebraic curves. We also give a matrix analogue of these results, where for a unimodular matrix A, we look at the greatest common
Computing torsion points on curves
 Experimental Math
"... Let X be a curve of genus g> 2 over a field k of characteristic 1. Introduction zero Let X ^ ^ A be an Albanese map associated to a point Po 2. Notation on X. The ManinMumford conjecture, first proved by Raynaud, ..."
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Let X be a curve of genus g> 2 over a field k of characteristic 1. Introduction zero Let X ^ ^ A be an Albanese map associated to a point Po 2. Notation on X. The ManinMumford conjecture, first proved by Raynaud,
TORSION POINTS ON CURVES
"... One of the themes of the summer school is the distribution of “special points ” on varieties. In Heath Brown’s lectures we study rational points on projective hypersurfaces; in Ullmo’s course we study Galois orbits and Duke’s lectures deal with CMpoints on the modular curve. This ..."
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One of the themes of the summer school is the distribution of “special points ” on varieties. In Heath Brown’s lectures we study rational points on projective hypersurfaces; in Ullmo’s course we study Galois orbits and Duke’s lectures deal with CMpoints on the modular curve. This
TORSION POINTS AND THE LATTÈS FAMILY
, 2014
"... We give a dynamical proof of a result of Masser and Zannier [MZ2, MZ3]: for any a 6 = b ∈ Q \ {0, 1}, there are only finitely many parameters t ∈ C for which points ..."
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We give a dynamical proof of a result of Masser and Zannier [MZ2, MZ3]: for any a 6 = b ∈ Q \ {0, 1}, there are only finitely many parameters t ∈ C for which points
Torsion points in families of Drinfeld modules
 Acta Arith
"... Abstract. Let Φ λ be an algebraic family of Drinfeld modules defined over a field K of characteristic p, and let a, b ∈ K [λ]. Assume that neither a(λ) nor b(λ) is a torsion point for Φ λ for all λ. If there exist infinitely many λ ∈ K such that both a(λ) and b(λ) are torsion points for Φ λ , then ..."
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Abstract. Let Φ λ be an algebraic family of Drinfeld modules defined over a field K of characteristic p, and let a, b ∈ K [λ]. Assume that neither a(λ) nor b(λ) is a torsion point for Φ λ for all λ. If there exist infinitely many λ ∈ K such that both a(λ) and b(λ) are torsion points for Φ λ
A finiteness property of torsion points
 HALF LOG DISCRIMINANT 11
"... Abstract. Let k be a number field, let E/k be an elliptic curve, and let S be a finite set of places of k containing the archimedean places. We prove that if α ∈ E(k) is nontorsion, then there are only finitely many torsion points ξ ∈ E(k)tors which are Sintegral with respect to α. We also prove an ..."
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Abstract. Let k be a number field, let E/k be an elliptic curve, and let S be a finite set of places of k containing the archimedean places. We prove that if α ∈ E(k) is nontorsion, then there are only finitely many torsion points ξ ∈ E(k)tors which are Sintegral with respect to α. We also prove
Torsion points on X0(N)
 IN AUTOMORPHIC FORMS, AUTOMORPHIC REPRESENTATIONS, AND ARITHMETIC, PROC. SYMPOS. PURE MATH
, 1999
"... Let N be a prime number, and let X be the modular curve X0(N), considered over the field of complex numbers. Suppose that the genus of X is at least 2, i.e., thatN is at least 23. Using the cusp at infinity onX, we identify X with a subvariety of positive codimension of the Jacobian of X. The set ..."
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of points onX which map to torsion points on the Jacobian is a finite set (ManinMumford conjecture) which always contains the two cusps onX and which contains the hyperelliptic branch points on X in the special case where X is hyperelliptic and N is different from 37. We conjecture that this set contains
Results 1  10
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1,142