%0 Journal Article
%T Determinant bundle in a family of curves, after A. Beilinson and V. Schechtman
%A H¨¦l¨¨ne Esnault
%A I-Hsun Tsai
%J Mathematics
%D 1999
%I arXiv
%R 10.1007/s002200050816
%X 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.
%U http://arxiv.org/abs/math/9910053v1