Esnault, HélèneHélèneEsnaultTsai, I-HsunI-HsunTsai2010-05-222018-06-282010-05-222018-06-28200000103616http://ntur.lib.ntu.edu.tw//handle/246246/183952https://www.scopus.com/inward/record.uri?eid=2-s2.0-0034349002&doi=10.1007%2fs002200050816&partnerID=40&md5=7c5adee3f66858e309037c543d556bf9Let 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.application/pdf55963 bytesapplication/pdfen-USjournal article2-s2.0-0034349002WOS:000087191600005http://ntur.lib.ntu.edu.tw/bitstream/246246/183952/1/08.pdf