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Torsion points on an algebraic subset of an affine torus (1996)
| Venue: | Internat. Math. Res. Notices |
| Citations: | 6 - 0 self |
BibTeX
@ARTICLE{Hironaka96torsionpoints,
author = {Eriko Hironaka},
title = {Torsion points on an algebraic subset of an affine torus},
journal = {Internat. Math. Res. Notices},
year = {1996},
pages = {953--982}
}
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Abstract
Work of Laurent and Sarnak, following a conjecture of Lang, shows that the number of torsion points of order n on an algebraic subset of an affine complex torus is polynomial periodic. In this paper, we find bounds on the degree and period of this number as a function of n. Some examples, including the number of n torsion points on Fermat curves, are computed to illustrate the methods. 1 Introduction. Let V ⊂ (C ∗ ) r be an algebraic subset. Laurent has shown that the torsion points on V lie on a finite union of translates of affine subtori contained in V. It follows that the number, pV (n), of torsion points of order n on V is polynomial periodic. In this paper, we find formulas and bounds for the degree and period of pV (n) in terms of defining equations for V.
