2016/07/21 by Sergio Estrada, Estrada, Sergio, Pedro A. Guil Asensio +4
Mathematics · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Rings, Modules, and Algebras #math.AG #math.CT #math.KT
paper · pdf · doi:10.48550/arxiv.1607.06529
18pp
openalex publication_date 2016/07/21 · arxiv created 2019/05/29 · arxiv updated 2019/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give sufficient conditions to ensure that the ideal Φ(\mathcal E) of \mathcal E-phantom maps in a locally λ-presentable exact category (A, E) is (special) (pre)covering ideal, where \mathcal E is an exact substructure of (A, E). As a byproduct, we infer the existence of various covering ideals in categories of sheaves which have a meaningful geometrical motivation. In particular we deal with a Zariski-local notion of phantom maps in categories of sheaves. We would like to point out that our approach is necessarily different from [FGHT13], as the categories involved in most of the examples we are interested in do not have enough projective morphisms.