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A model structure approach to the finitistic dimension conjectures |
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| Authors: | M. Cortés Izurdiaga S. Estrada P. A. Guil Asensio |
| Affiliation: | 1. Departamento de álgebra y Análisis Matemático, Universidad de Almería, Almería, 04071, Spain;2. Departamento de Matemática Aplicada, Universidad de Murcia, Campus del Espinardo, Espinardo (Murcia), 30100, Spain;3. Departamento de Matemáticas, Universidad de Murcia, Campus del Espinardo, Espinardo (Murcia), 30100, Spain |
| Abstract: | We explore the interlacing between model category structures attained to classes of modules of finite $mathcal {X}$‐dimension, for certain classes of modules $mathcal {X}$. As an application we give a model structure approach to the finitistic dimension conjectures and present a new conceptual framework in which these conjectures can be studied. |
| Keywords: | Finitistic conjectures model categories relative dimensions MSC (2010) Primary: 16D90 16E30 Secondary: 55U35 18G35 |