New enhancements of derived categories of coherent sheaves and\n applications

2014/06/29 by Valery A. Lunts, Lunts, Valery A., Olaf M. Schnürer +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Category Theory (math.CT) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1406.7559

openalex publication_date 2014/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce new enhancements for the bounded derived category D^b(Coh(X))\nof coherent sheaves on a suitable scheme X and for its subcategory Perf(X)\nof perfect complexes. They are used for translating Fourier-Mukai functors to\nfunctors between derived categories of dg algebras, for relating homological\nsmoothness of Perf(X) to geometric smoothness of X, and for proving\nhomological smoothness of D^b(Coh(X)). Moreover, we characterize properness\nof Perf(X) and D^b(Coh(X)) geometrically.\n

Related

• Derived categories of coherent sheaves on some zero-dimensional schemes
• Derived categories of coherent sheaves
• Twisted Fourier-Mukai functors
• Triangulated endofunctors of the derived category of coherent sheaves which do not admit DG liftings
• Descent of coherent sheaves and complexes to geometric invariant theory quotients