Nilpotent invariance of semi-topological K-theory of dg-algebras and the lattice conjecture

Abstract

We show existence of a natural rational structure on periodic cyclic homology, conjectured by L. Katzarkov, M. Kontsevich, T. Pantev, for several classes of dg-categories, including proper connective $\mathbb{C}$-dg-algebras and dg-categories of local systems. The main ingredient is derived nilpotent invariance of A. Blanc's semi-topological K-theory, which we establish along the way.

arXiv comment20 pages. Comments welcome

References in corpus (5)

• The K-theoretic Farrell-Jones Conjecture for hyperbolic groups
• Microlocal Morse theory of wrapped Fukaya categories
• Differential Graded Categories are k-linear Stable Infinity Categories
• The Farrell-Jones isomorphism conjecture for 3-manifold groups
• Algebraic $K$-theory, assembly maps, controlled algebra, and trace methods

Cited by in corpus (1)

• On nilpotent extensions of $\infty$-categories and the cyclotomic trace