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Bismut, Jean-Michel; Lebeau, Gilles

Complex immersions and Quillen metrics. (English) Zbl 0784.32010

Publ. Math., Inst. Hautes Étud. Sci. 74, 1-297 (1991).
The authors’ work is devoted to the proof of a certain (integral) formula which is an essential ingredient in the arithmetic Riemann-Roch of Gillet and Soulé. This integral formula is an expression for the logarithm of the norm (with respect to Quillen metrics) of a certain canonical section associated to determinant line bundles of a vector bundle on \(Y\) and a resolution of it with respect to a complex immersion \(Y\hookrightarrow X\). The integrals contain Todd classes and the additive genus \(R(x)\) of Gillet and Soulé.
The paper is clearly written, very well organized and essentially self- contained. For this reason it is also accessable to non-experts.
Reviewer: S.Kosarew (Saint-Martin-d’Hères)

Cited in 16 Reviews
Cited in 104 Documents

MSC:

32C35 Analytic sheaves and cohomology groups
14C40 Riemann-Roch theorems

Keywords:

arithmetic Riemann-Roch; Quillen metrics; analytic torsion
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Full Text: DOI Numdam EuDML

References:

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