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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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A Lindemann-Weierstrass theorem for semi-abelian varieties over function fields
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by Daniel Bertrand and Anand Pillay PDF
J. Amer. Math. Soc. 23 (2010), 491-533 Request permission


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
  • MR Author ID: 139610
  • 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
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 23 (2010), 491-533
  • MSC (2000): Primary 12H05, 14K05, 03C60, 34M15, 11J95
  • DOI:
  • MathSciNet review: 2601041