Théories de Galois différentielles et transcendance
Annales de l'Institut Fourier, Tome 59 (2009) no. 7, pp. 2773-2803.

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

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.

DOI : https://doi.org/10.5802/aif.2507
Classification : 12H05,  14K05,  03C60,  34M15,  11J95
Mots clés : théorie de Galois différentielle, indépendance algébrique, variétés abéliennes, cohomologie galoisienne, connexion de Gauss-Manin, dérivées logarithmiques
@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},
     pages = {2773--2803},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {59},
     number = {7},
     year = {2009},
     doi = {10.5802/aif.2507},
     mrnumber = {2649338},
     language = {fr},
     url = {http://archive.numdam.org/articles/10.5802/aif.2507/}
}
Bertrand, Daniel. Théories de Galois différentielles et transcendance. Annales de l'Institut Fourier, Tome 59 (2009) no. 7, pp. 2773-2803. doi : 10.5802/aif.2507. http://archive.numdam.org/articles/10.5802/aif.2507/

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