On the Existence of a Compact Generator on the Derived Category of a Noetherian Formal Scheme |
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| Authors: | Leovigildo Alonso Tarrío Ana Jeremías López Marta Pérez Rodríguez María J Vale Gonsalves |
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| Institution: | 1.Departamento de álxebra, Facultade de Matemáticas,Universidade de Santiago de Compostela,Santiago de Compostela,Spain;2.Departamento de Matemáticas, Esc. Sup. de Enx. Informática, Campus de Ourense,Universidade de Vigo,Ourense,Spain |
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| Abstract: | In this paper, we prove that for a noetherian formal scheme
\mathfrak X\mathfrak X, its derived category of sheaves of modules with quasi-coherent torsion homologies
Dqct(\mathfrak X)\boldsymbol{\mathsf{D}}_\mathsf{qct}(\mathfrak X) is generated by a single compact object. In an Appendix we prove that the category of compact objects in
Dqct(\mathfrak X)\boldsymbol{\mathsf{D}}_\mathsf{qct}(\mathfrak X) is skeletally small. |
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