Théories de Galois différentielles et transcendance

Bertrand, Daniel

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.

Classification : 12H05, 14K05, 03C60, 34M15, 11J95
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

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