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This article discusses a conjectural description of the Lie algebra of the differential Galois group attached to a linear differential equation as being the smallest algebraic Lie algebra whose reduction mod p contains, for almost all p, the p-curvature of the reduction mod p of the differential equation in question. RESUME. On discute une description conjecturale de Falgebre de Lie du groupe de Galois differentiel d'une equation differentielle lineaire comme etant la plus petite algebre de Lie algebrique dont la reduction modulo p contient, pour presquc tout p. la p-courbure de la reduction modulo p de Inequation differentielle dont il s'agit.

A conjecture in the arithmetic theory of differential equations