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

Bertrand, Daniel ¹   ; Pillay, Anand ²

¹ Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, Case 247, 4, Place Jussieu, F-75252 Paris Cedex 05, France
² School of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom

Journal of the American Mathematical Society, Tome 23 (2010) no. 2, pp. 491-533

Résumé

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.

Détail

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

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