  Relying on the formalism developed by Alexander Beilinson and Takeshi Saito,
we compute the characteristic cycle of an external symmetric power of a tame
\'etale sheaf on a curve. This generalizes a result of G\'erard Laumon in
characteristic 0 and leads to a result of local acyclicity of the Abel-Jacobi
morphism, due to Pierre Deligne and motivated by his geometric approach to the
product formula for the determinant of cohomology (epsilon factor).
