Determinant bundle in a family of curves, after A. Beilinson and V. Schechtman
Algebraic Geometry
2009-10-31 v1
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 \'etale multisection. We analyse this and correct a point in the original proof.
Keywords
Cite
@article{arxiv.math/9910053,
title = {Determinant bundle in a family of curves, after A. Beilinson and V. Schechtman},
author = {Hélène Esnault and I-Hsun Tsai},
journal= {arXiv preprint arXiv:math/9910053},
year = {2009}
}
Comments
6 pages, Latex 2e