Let G be a commutative algebraic group defined over a number field K that is disjoint over K from and satisfies the condition of semistability. Consider a linear form l on the Lie algebra of G with algebraic coefficients and an algebraic point u in a p-adic neighbourhood of the origin with the condition that l does not vanish at u. We give a lower bound for the p-adic absolute value of l(u) which depends up to an effectively computable constant only on the height of the linear form, the height of the point u and p.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-2-2,
author = {Clemens Fuchs and Duc Hiep Pham},
title = {Commutative algebraic groups and p-adic linear forms},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {115-147},
zbl = {06446120},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-2-2}
}
Clemens Fuchs; Duc Hiep Pham. Commutative algebraic groups and p-adic linear forms. Acta Arithmetica, Tome 168 (2015) pp. 115-147. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-2-2/