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arXiv · 1212.3264

Resolutions in factorization categories

Matthew Ballard·Dragos Deliu·David Favero·M. Umut Isik·Ludmil Katzarkov
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Abstract

Generalizing Eisenbud's matrix factorizations, we define factorization categories. Following work of Positselski, we define their associated derived categories. We construct specific resolutions of factorizations built from a choice of resolutions of their components. We use these resolutions to lift fully-faithfulness statements from derived categories of Abelian categories to derived categories of factorizations and to construct a spectral sequence computing the morphism spaces in the derived categories of factorizations from Ext-groups of their components in the underlying Abelian category.

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Matthew Ballard, Dragos Deliu, David Favero, M. Umut Isik, Ludmil Katzarkov. 2012-12-13. Resolutions in factorization categories. https://arxiv.org/abs/1212.3264

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