Determinant Bundle in a Family of Curves,?after A. Beilinson and V. Schechtman
Resource
Communications in Mathematical Physics 211 (2): 359-363
Journal
Communications in Mathematical Physics
Journal Volume
211
Journal Issue
2
Pages
359-363
Date Issued
2000
Date
2000
Author(s)
Esnault, Hélène
Abstract
Let π : X → S be a smooth projective family of curves over a smooth base S over a field of characteristic 0, together with a bundle E on X. Then A. Beilinson and V. Schechtman define in [1] a beautiful "trace complex" trA•E on X, the 0th relative cohomology of which describes the Atiyah algebra of the determinant bundle of E on S. Their proof reduces the general case to the acyclic one. In particular, one needs a comparison of Rπ*(trA•F) for F = E and F = E(D), where D is étale over S (see Theorem 2.3.1, reduction ii) in [1]). In this note, we analyze this reduction in more detail and correct a point.
Type
journal article
File(s)![Thumbnail Image]()
Loading...
Name
08.pdf
Size
23.52 KB
Format
Adobe PDF
Checksum
(MD5):84c84affcd5c8fd992516d7b83dc2fdc