  In 1985, Yu. V. Nesterenko produced a criterion for linear independence,
which is a variant of Siegel's. While Siegel uses upper bounds on full systems
of forms, Nesterenko uses upper and lower bounds on sufficiently dense
sequences of individual forms. The proof of Nesterenko's criterion was
simplified by F. Amoroso and P. Colmez in 2003. More recently, S. Fischler and
W. Zudilin produced a refinement, together with a much simpler proof. This new
proof rests on a simple argument which we expand here. We get a new result,
which contains Nesterenko's criterion, as well as criteria for algebraic
independence.
