Kernels for Noncommutative Projective Schemes

2017/09/19 by Ballard, Matthew R., Farman, Blake A.
#14A22 #16D90 #16E35 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1709.06470

Abstract

We give a noncommutative geometric description of the internal Hom dg-category in the homotopy category of dg-categories between two noncommutative projective schemes in the style of Artin-Zhang. As an immediate application, we give a noncommutative projective derived Morita statement along lines of Rickard and Orlov.

Related

• Künneth and extension theorems for Morita invariants of non-commutative schemes
• On derived categories and noncommutative motives of varieties
• Bondal-Orlov's reconstruction theorem in noncommutative projective geometry
• The homotopy theory of dg-categories and derived Morita theory
• An introduction to Noncommutative Projective Geometry