TL;DR
This paper develops a unified framework for transfer maps and projection formulas within dg categories, enabling their application across various algebraic and topological invariants.
Contribution
It introduces a non-commutative approach to transfer maps and projection formulas, extending their applicability to multiple (co)homology theories.
Findings
Unified treatment of transfer maps and projection formulas in dg categories
Application to algebraic K-theory, cyclic homology, and topological cyclic homology
Facilitates computations in non-commutative geometry and scheme invariants
Abstract
Transfer maps and projection formulas are undoubtedly one of the key tools in the development and computation of (co)homology theories. In this note we develop an unified treatment of transfer maps and projection formulas in the non-commutative setting of dg categories. As an application, we obtain transfer maps and projection formulas in algebraic K-theory, cyclic homology, topological cyclic homology, and other scheme invariants.
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