  In Comm. Math. Physics 118 (1988), 651-701, A. Beilinson and V. Schechtman
define on the total space of a smooth family of curves a so-called trace
complex associated to a vector bundle, the 0-th relative cohomology of which is
the Atiyah algebra of the determinant bundle. Their proof reduces the general
case to the acyclic one. In particular, one needs a comparison of the image of
the trace complex for a bundle, and its twist by an \'etale multisection. We
analyse this and correct a point in the original proof.
