Kernels for Noncommutative Projective Schemes

TL;DR

This paper develops a noncommutative geometric framework for understanding internal Hom dg-categories between noncommutative projective schemes, leading to a derived Morita equivalence in the noncommutative setting.

Contribution

It introduces a noncommutative geometric description of internal Hom dg-categories and establishes a noncommutative projective derived Morita equivalence.

Findings

Noncommutative geometric description of internal Hom dg-categories.

Derived Morita equivalence for noncommutative projective schemes.

Extension of classical Morita theory to noncommutative projective geometry.

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.