Abstract
The purpose of this note is to remark that Theorem 3.7 in [1], when combined with the work of Bismut and Freed [2], leads, in the algebraic case, to an improvement of both results concerning the holonomy of determinant line bundles.
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Gillet, H., Soulé, C.: Arithmetic Chow groups and differential characters. In: AlgebraicK-theory: connections with geometry and topology. Jardine, J.F., Snaith, V.P. (eds.), pp. 30–68. Dordrecht: Kluwer Academic 1989
Bismut, J.-M., Freed,D.-S.: The analysis of elliptic families. II. Dirac operators, êta invariants and the holonomy theorem. Commun. Math. Phys.107, 103–163 (1986)
Bismut, J.-M., Gillet, H., Soulé, C.: Analytic torsion and holomorphic determinant bundles. I–III. Commun. Math. Phys.115, 49–78, 78–126, 301–351 (1988)
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Communicated by A. Jaffe
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Gillet, H., Soule, C. The holonomy of the determinant of cohomology of an algebraic bundle. Commun.Math. Phys. 131, 219–220 (1990). https://doi.org/10.1007/BF02097685
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DOI: https://doi.org/10.1007/BF02097685