A Lindemann-Weierstrass theorem for semi-abelian varieties over function fields

Bertrand, Daniel; Pillay, Anand

doi:10.1090/S0894-0347-09-00653-5

A Lindemann-Weierstrass theorem for semi-abelian varieties over function fields
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by Daniel Bertrand and Anand Pillay

J. Amer. Math. Soc. 23 (2010), 491-533

DOI: https://doi.org/10.1090/S0894-0347-09-00653-5

Published electronically: December 2, 2009

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Abstract:

We prove an analogue of the Lindemann-Weierstrass theorem (that the exponentials of a $\mathbb {Q}$-linearly independent set of algebraic numbers are algebraically independent), replacing $\mathbb {Q}^{alg}$ by $\mathbb {C}(t)^{alg}$ and $\mathbb {G}_{m}^{n}$ by a semi-abelian variety over $\mathbb {C}(t)^{alg}$. Both the formulations of our results and the methods are differential algebraic in nature.

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