Abstract: The Dundas-Goodwillie-McCarthy (DGM) theorem asserts that the difference between the K-theory of a ring and its thickening is the same as the difference in topological cyclic homology (TC). This has had spectacular applications in computations for K-theory as well as inspiring recent developments in p-adic Hodge theory. According to Bondal and van den Bergh, the category of perfect complexes on a qcqs scheme is equivalent to the category of perfect complexes on a $A_{\infty}$-ring. Therefore, the DGM theorem is applicable in this geometric context.

However, the category of perfect complexes on algebraic stacks do not enjoy this "monogenic generation" property. In joint work with Vova Sosnilo. we proved a version of the DGM theorem where this is applicable in many cases. I will explain how the proof works, whose new input comes from Bondarko's theory of weights (aka co-t-structures), and also some applications.