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.
Mot clés : théorie de Galois différentielle, indépendance algébrique, variétés abéliennes, cohomologie galoisienne, connexion de Gauss-Manin, dérivées logarithmiques
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},
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://www.numdam.org/articles/10.5802/aif.2507/}
}
TY - JOUR AU - Bertrand, Daniel TI - Théories de Galois différentielles et transcendance JO - Annales de l'Institut Fourier PY - 2009 SP - 2773 EP - 2803 VL - 59 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2507/ DO - 10.5802/aif.2507 LA - fr ID - AIF_2009__59_7_2773_0 ER -
%0 Journal Article %A Bertrand, Daniel %T Théories de Galois différentielles et transcendance %J Annales de l'Institut Fourier %D 2009 %P 2773-2803 %V 59 %N 7 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2507/ %R 10.5802/aif.2507 %G fr %F AIF_2009__59_7_2773_0
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://www.numdam.org/articles/10.5802/aif.2507/
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