Théories de Galois différentielles et transcendance  [ Differential Galois theories and transcendence ]
Annales de l'Institut Fourier, Volume 59 (2009) no. 7, p. 2773-2803

We survey recent work on the exponential and logarithmic cases of the functional Schanuel conjecture. Using various differential Galois theories, we present parallel (and sometimes new) proofs in the case of abelian varieties.

On décrit des preuves galoisiennes des versions logarithmique et exponentielle de la conjecture de Schanuel, pour les variétés abéliennes sur un corps de fonctions.

DOI : https://doi.org/10.5802/aif.2507
Classification:  12H05,  14K05,  03C60,  34M15,  11J95
Keywords: Differential Galois theory, algebraic independence, abelian varieties, Galois cohomology, Gauss-Manin connections, logarithmic derivatives
@article{AIF_2009__59_7_2773_0,
     author = {Bertrand, Daniel},
     title = {Th\'eories de Galois diff\'erentielles et transcendance},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {59},
     number = {7},
     year = {2009},
     pages = {2773-2803},
     doi = {10.5802/aif.2507},
     mrnumber = {2649338},
     zbl = {pre05689406},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2009__59_7_2773_0}
}
Bertrand, Daniel. Théories de Galois différentielles et transcendance. Annales de l'Institut Fourier, Volume 59 (2009) no. 7, pp. 2773-2803. doi : 10.5802/aif.2507. http://www.numdam.org/item/AIF_2009__59_7_2773_0/

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