Determinant bundle in a family of curves, after A. Beilinson and V. Schechtman
arXiv:math/9910053 · doi:10.1007/s002200050816
Abstract
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 étale multisection. We analyse this and correct a point in the original proof.
6 pages, Latex 2e