A type of comparison theorem in polynomial growth cohomology
type: Item
instance of: scholarly article
title: A type of comparison theorem in polynomial growth cohomology
zbMATH Open document ID: 0545.32007
author: Nobuo Sasakura
published in: Proceedings of the Japan Academy. Series A
publication date: 1983-01-01T00:00:00Z
review text: This note is a continuation of our previous paper on stratification theory and cohomology with some structures (growth and division), which was applied to give a generalization of the algebraic and analytic de Rham theorems of A. Grothendieck [the author, ''Cohomology with polynomial growth and completion theory'', Publ. Res. Inst. Math. Sci. 17, 371-552 (1981)]. In the present note, we point out that a type of a GAGA comparison is given in terms of polynomial growth cohomology and a stratification theory. This may be a generalization of the original GAGA comparison of \textit{J.-P. Serre} [Ann. Inst. Fourier 6(1955/56), 1-42 (1956; Zbl 0075.304)] (for a projective variety) and similar comparisons for locally free sheaves over a quasi projective variety [\textit{M. Cornalba} and \textit{D. Griffiths}, Invent. Math. 28, 1-106 (1975; Zbl 0293.32026)] and \textit{G. Maltsiniotis} (after \textit{P. Deligne}) [Sémin. Géométrie analytique Éc. Norm. Super. 1972-1973, Astérisque 17, 141-160 (1974; Zbl 0297.14006)]. The fundamental importance of the stratification theory for analytic varieties has been well known and is increasing. The stratification theoretical cohomology group \(H_{str}\) (in the paper under review) may be useful for some global treatments of coherent sheaves and other analytic objects on analytic varieties. As I mentioned in the present paper, the stratification theoretical method works well for some explicit constructions of holomorphic bundles [''A stratification theoretical method of construction of holomorphic vector bundles'', submitted to Proc. U.S.-Japan Semin. Singularities, held at July, 1984].
Mathematics Subject Classification ID: 32C35
Mathematics Subject Classification ID: 32S60
Mathematics Subject Classification ID: 32J25
zbMATH DE Number: 3867713
zbMATH Keywords: polynomial growth cohomology
zbMATH Keywords: stratification
MaRDI profile type: Publication
full work available at URL: pjaa.59.297
OpenAlex ID: W2091519474
cites work: Analytic cycles and vector bundles on non-compact algebraic varieties
cites work: Equations différentielles à points singuliers réguliers
cites work: Q4050714
cites work: Cohomology with polynomial growth and completion theory
cites work: Q4133921
cites work: Quantitative properties of analytic varieties complex analytic de Rham cohomology, II
cites work: Evolving fuzzy \(\mathbb C\mathbb P^n\) and lattice \(n\)-simplex
cites work: Algebraic geometry and analytic geometry
DOI: 10.3792/PJAA.59.297
Recommended article: Cohomology with polynomial growth and completion theory
Recommended article: Cohomological comparison theorem
Recommended article: On the cohomology comparison theorem
Recommended article: A comparison theorem in p-adic cohomology
Recommended article: Teoremi di paragone in geometria algebrica
Recommended article: Q4392684
Recommended article: Relative cohomology of polynomial mappings
Recommended article: Q4694942
Recommended article: Two comparison theorems in étale cohomology; applications
description: scientific article; zbMATH DE number 3867713