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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2017: 0.23

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Volume 11, Issue 4


More on Descent Theory for Schemes

B. Mesablishvili
  • A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, M. Aleksidze St., Tbilisi 0193, Georgia. E-mail:
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Published Online: 2010-03-03 | DOI: https://doi.org/10.1515/GMJ.2004.783


In this paper we continue the investigation of some aspects of descent theory for schemes that was begun in [Mesablishvili, Appl. Categ. Structures]. Let 𝐒𝐂𝐇 be a category of schemes. We show that quasi-compact pure morphisms of schemes are effective descent morphisms with respect to 𝐒𝐂𝐇-indexed categories given by (i) quasi-coherent modules of finite type, (ii) flat quasi-coherent modules, (iii) flat quasi-coherent modules of finite type, (iv) locally projective quasicoherent modules of finite type. Moreover, we prove that a quasi-compact morphism of schemes is pure precisely when it is a stable regular epimorphism in 𝐒𝐂𝐇. Finally, we present an alternative characterization of pure morphisms of schemes.

Key words and phrases:: Scheme; pure morphism; descent theory

About the article

Received: 2004-05-10

Revised: 2004-10-06

Published Online: 2010-03-03

Published in Print: 2004-12-01

Citation Information: Georgian Mathematical Journal, Volume 11, Issue 4, Pages 783–800, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/GMJ.2004.783.

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