Transfer maps and projection formulas (Q2845533)

A differential graded (dg) category over a base commutative ring \(k\) is a category enriched over complexes of \(k\)-modules (morphism sets are complexes) in such a way that composition fulfills the Leibniz rule: \(d(fg)=(df)g+(-1)^{\mathrm{deg}(f)}f(dg)\). Transfer maps and projection formulas are undoubtedly key tools in the development and computation of (co)homology theories. In this paper the author develops a unified treatment of transfer maps and projection formulas in the noncommutative setting of dg categories. As an application, the author obtains transfer maps and projection formulas in algebraic \(K\)-theory, cyclic homology, topological cyclic homology, and other scheme invariants.