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ISSN 1088-6834(e) ISSN 0894-0347(p)

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

Author(s): Daniel Bertrand; Anand Pillay
Journal: J. Amer. Math. Soc. 23 (2010), 491-533.
MSC (2000): Primary 12H05, 14K05, 03C60, 34M15, 11J95
Posted: December 2, 2009
MathSciNet review: 2601041
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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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