TY - JOUR
T1 - On abelian multiplicatively dependent points on a curve in a torus
AU - Ostafe, Alina
AU - Sha, Min
AU - Shparlinski, Igor E.
AU - Zannier, Umberto
PY - 2018/6/1
Y1 - 2018/6/1
N2 - We show, under some natural conditions, that the set of abelian (and thus also cyclotomic) multiplicatively dependent points on an irreducible curve over a number field is a finite union of preimages of roots of unity by a certain finite set of primitive characters from Gmn to Gm restricted to the curve, and a finite set. We also introduce the notion of primitive multiplicative dependence and obtain a finiteness result for primitively multiplicatively dependent points defined over a so-called Bogomolov extension of a number field.
AB - We show, under some natural conditions, that the set of abelian (and thus also cyclotomic) multiplicatively dependent points on an irreducible curve over a number field is a finite union of preimages of roots of unity by a certain finite set of primitive characters from Gmn to Gm restricted to the curve, and a finite set. We also introduce the notion of primitive multiplicative dependence and obtain a finiteness result for primitively multiplicatively dependent points defined over a so-called Bogomolov extension of a number field.
UR - http://www.scopus.com/inward/record.url?scp=85048628979&partnerID=8YFLogxK
U2 - 10.1093/qmath/hax045
DO - 10.1093/qmath/hax045
M3 - Article
AN - SCOPUS:85048628979
VL - 69
SP - 391
EP - 401
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
SN - 0033-5606
IS - 2
ER -