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Mathematics of Computation

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Computing the torsion points of a variety defined by lacunary polynomials

Author: Louis Leroux
Journal: Math. Comp. 81 (2012), 1587-1607
MSC (2010): Primary 11Y16; Secondary 12Y05, 68W30
Published electronically: October 21, 2011
MathSciNet review: 2904592
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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.

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Additional Information

Louis Leroux
Affiliation: Laboratoire de Mathematiques Nicolas Oresme, Univerite de Caen BP 5186, 14032 Caen cedex, France

Received by editor(s): December 3, 2009
Received by editor(s) in revised form: March 21, 2011
Published electronically: October 21, 2011
Additional Notes: The author was partially supported by the CNRS PICS “Properties of heights of arithmetic varieties”, (2009-2011).
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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