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Formule pour l’indice des complexes constructibles et des modules holonomes. (A formula for the index of constructible complexes and holonomic modules). Erratum. (French) Zbl 0605.14018

Let M denote a compact complex manifold and \({\mathcal M}^ a \)holonomic module on \(M\). The global index \(\chi({\mathcal M})\) is defined to be the Euler-Poincaré characteristic of the hypercohomology of the de Rham complex. The main result is that \(\chi({\mathcal M})\) is equal to the degree of 0-cycle \((-1)^{\dim M}[Ch({\mathcal M})\cdot [M]]\), where \(Ch({\mathcal M})\) denotes the characteristical cycle of \({\mathcal M}\). An algebraic proof of this formula in the algebraic case was given by G. Laumon in Algebr. Geom., Proc. Jap.-Fr. Conf., Tokyo and Kyoto 1982, Lect. Notes Math. 1016, 151-237 (1983; Zbl 0551.14006). This formula as well as its local and relative variants hold more generally for any bounded sheaf with constructible cohomology sheaves.
In the erratum are given the corrections of some typographical errors.
Reviewer: H.Lange

MSC:

14F40 de Rham cohomology and algebraic geometry
32C38 Sheaves of differential operators and their modules, \(D\)-modules
14C25 Algebraic cycles

Citations:

Zbl 0551.14006
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