Moderate and formal cohomology associated with constructible sheaves. (English) Zbl 0881.58060

Kashiwara, Masaki; Schapira, Pierre

Mém. Soc. Math. Fr., Nouv. Sér. 64, III, 76 p. (1996).

In Mikio Sato’s spirit of “Algebraic Analysis” this paper is concerned with a systematic study of the functor \(-{\overset {w} \otimes} {\mathcal O}_X\) of formal cohomology, as well as the earlier considered functor \(\text{Thom} (-,{\mathcal O}_X)\) of temperate cohomology [cf. E. Andronikof, Mém. Soc. Math. Fr. Nouv. Sér. 57, 178 pp. (1994; Zbl 0805.58059); Z. Mebkhout in Lect. Notes Phys. 126, 90-110 (1980; Zbl 0444.32003); the first named author, Publ. Res. Inst. Math. Sci. 20, 319-365 (1984; Zbl 0566.32023)], where \(X\) is a suitable manifold. They are constructed following an extension pattern, from the category of \(\mathbb{R}\)-constructible sheaves to that of \(D_X\)-modules. The main results are the adjunction formulae obtained for correspondences of complex manifolds, meaningful to integral geometry.
As a further application the authors promise a functorial treatment of integral transformations with growth conditions.

Reviewer: G.F.Nassopoulos (Athens)

MSC:

58J15	Relations of PDEs on manifolds with hyperfunctions
46F20	Distributions and ultradistributions as boundary values of analytic functions
18E30	Derived categories, triangulated categories (MSC2010)
32S60	Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)

Keywords:

formal cohomology; temperate cohomology; constructible sheaves; adjunction formulae; correspondences of complex manifolds

Citations:

Zbl 0805.58059; Zbl 0444.32003; Zbl 0566.32023

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