Computing the torsion points of a variety defined by lacunary polynomials

Abstract

Abstract. We present an algorithm for computing the set of torsion points satisfying a given system of multivariate polynomial equations. Its complexity is quasilinear in the logarithm of the degree and in the height of the input equations but exponential in their number of variables and nonzero terms.

Groups generated by iterations of polynomials over finite fields

“…Finally, for a Laurent polynomial We also refer to [1,15,17] for some generalizations and related questions on torsion points on curves and varieties.…”

“…we denote by V (F ) the area of the Newton polytope N (F ) of F , which is defined as the convex hull of the set {(i, j): a i,j = 0}. We use the following result of Beukers We also refer to [1,15,17] for some generalizations and related questions on torsion points on curves and varieties.…”

Elements of large order on varieties over prime finite fields

“…We also note the work of [18] is related to some algorithmic aspects of finding torsion points. We also use the following result of Beukers and Smyth [3, Section 4.1].…”

Cyclotomic Points and Algebraic Properties of Polygon Diagonals

“…This has since been extended by Beukers and Smyth to the setting of algebraic plane curves [BS02], and generalized to arbitrary dimensions by Aliev and Smith [AS12]. These papers will form the backbone of our results; those interested in further constructive results and explicit methods may additionally explore [Ler12], [Roj07], and [Rup93].…”