Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

Descent of restricted flat Mittag-Leffler modules and generalized vector bundles


Authors: Sergio Estrada, Pedro Guil Asensio and Jan Trlifaj
Journal: Proc. Amer. Math. Soc. 142 (2014), 2973-2981
MSC (2010): Primary 14F05, 16D40; Secondary 03E35, 13D07, 18E15, 55N30
Published electronically: May 22, 2014
MathSciNet review: 3223352
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A basic question for any property of quasi-coherent sheaves on a scheme $ X$ is whether the property is local, that is, it can be defined using any open affine covering of $ X$. Locality follows from the descent of the corresponding module property: for (infinite dimensional) vector bundles and Drinfeld vector bundles, it was previously proved by Kaplansky's technique of dévissage. Since vector bundles coincide with $ \aleph _0$-restricted Drinfeld vector bundles, a question arose as to whether locality holds for $ \kappa $-restricted Drinfeld vector bundles for each infinite cardinal $ \kappa $. We give a positive answer here by replacing the dévissage with its recent refinement involving $ \mathcal C$-filtrations and the Hill Lemma.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14F05, 16D40, 03E35, 13D07, 18E15, 55N30

Retrieve articles in all journals with MSC (2010): 14F05, 16D40, 03E35, 13D07, 18E15, 55N30


Additional Information

Sergio Estrada
Affiliation: Departamento de Matemática Aplicada, Universidad de Murcia, Campus del Espin- ardo 30100, Murcia, Spain
Email: sestrada@um.es

Pedro Guil Asensio
Affiliation: Departamento de Matemáticas, Universidad de Murcia, Campus del Espinardo 30100, Murcia, Spain
Email: paguil@um.es

Jan Trlifaj
Affiliation: Faculty of Mathematics and Physics, Department of Algebra, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic
Email: trlifaj@karlin.mff.cuni.cz

DOI: https://doi.org/10.1090/S0002-9939-2014-12056-9
Keywords: Descent, restricted Drinfeld vector bundle, Mittag--Leffler module, $\mathcal C$--filtration, Whitehead module
Received by editor(s): October 14, 2011
Received by editor(s) in revised form: September 24, 2012
Published electronically: May 22, 2014
Additional Notes: The first author was partially supported by DGI MTM2008-03339, by the Fundación Seneca and by the Junta de Andalucía, Consejería de Economía, Innovación y Ciencia and FEDER funds
The third author was supported by GAČR 201/09/0816 and MSM 0021620839
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.