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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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


Authors: Daniel Bertrand and Anand Pillay
Journal: J. Amer. Math. Soc. 23 (2010), 491-533
MSC (2000): Primary 12H05, 14K05, 03C60, 34M15, 11J95
Published electronically: December 2, 2009
MathSciNet review: 2601041
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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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Additional Information

Daniel Bertrand
Affiliation: Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, Case 247, 4, Place Jussieu, F-75252 Paris Cedex 05, France

Anand Pillay
Affiliation: School of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom

DOI: http://dx.doi.org/10.1090/S0894-0347-09-00653-5
PII: S 0894-0347(09)00653-5
Keywords: Algebraic independence, differential algebraic groups, logarithmic derivatives, Gauss-Manin connections, differential Galois theory.
Received by editor(s): October 24, 2008
Published electronically: December 2, 2009
Additional Notes: The second author was supported by a Marie Curie Chair and an EPSRC grant
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.