Morita Theory - Interplay Between DG and Weakly Approximable Triangulated Categories

Explore a comprehensive lecture on Morita theory for schemes, focusing on the interplay between dg and weakly approximable triangulated categories. Delve into a significant generalization of Rickard's result beyond the affine setting, examining the proof that combines techniques from dg enhancements and the new theory of weakly approximable triangulated categories. Discover how this approach allows for the intrinsic description of subcategories of weakly approximable triangulated categories. Learn about additional applications to the categories of singularities in this joint work in progress with A. Canonaco and A. Neeman. Gain insights into the celebrated result by Rickard, which demonstrates how derived Morita equivalence for two coherent rings can be detected through various naturally associated triangulated categories, such as perfect complexes and bounded or unbounded derived categories of (finitely) generated modules.