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Determinant bundle in a family of curves, after A. Beilinson and V. Schechtman

Hélène Esnault·I-Hsun Tsai
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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.

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Hélène Esnault, I-Hsun Tsai. 1999-10-09. Determinant bundle in a family of curves, after A. Beilinson and V. Schechtman. https://doi.org/10.1007/s002200050816

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