Descent of restricted flat Mittag–Leffler modules and generalized vector bundles
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- by Sergio Estrada, Pedro Guil Asensio and Jan Trlifaj PDF
- Proc. Amer. Math. Soc. 142 (2014), 2973-2981 Request permission
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
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Additional Information
- Sergio Estrada
- Affiliation: Departamento de Matemática Aplicada, Universidad de Murcia, Campus del Espin- ardo 30100, Murcia, Spain
- MR Author ID: 711614
- 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
- MR Author ID: 174420
- ORCID: 0000-0001-5773-8661
- Email: trlifaj@karlin.mff.cuni.cz
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 2973-2981
- MSC (2010): Primary 14F05, 16D40; Secondary 03E35, 13D07, 18E15, 55N30
- DOI: https://doi.org/10.1090/S0002-9939-2014-12056-9
- MathSciNet review: 3223352