
arXiv: 1404.4209
Let $G$ be a commutative algebraic group defined over a number field $K$ that is disjoint over $K$ to $\mathbb G_a$ 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 $p$.
This is a preprint of the Materials accepted for publication in "Acta Arithmetica"
Mathematics - Number Theory, 11G99 (Primary) 14L10, 11J86 (Secondary), Approximation in non-Archimedean valuations, heights, Arithmetic algebraic geometry (Diophantine geometry), Mathematics - Algebraic Geometry, effective results, FOS: Mathematics, linear forms, Number Theory (math.NT), Group varieties, Algebraic Geometry (math.AG), Linear forms in logarithms; Baker's method, commutative algebraic groups
Mathematics - Number Theory, 11G99 (Primary) 14L10, 11J86 (Secondary), Approximation in non-Archimedean valuations, heights, Arithmetic algebraic geometry (Diophantine geometry), Mathematics - Algebraic Geometry, effective results, FOS: Mathematics, linear forms, Number Theory (math.NT), Group varieties, Algebraic Geometry (math.AG), Linear forms in logarithms; Baker's method, commutative algebraic groups
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