Singular coefficients in the K-theoretic Farrell-Jones conjecture

Abstract

Let G be a group and k a field of characteristic zero. We prove that if the Farrell-Jones conjecture for the K-theory of R[G] is satisfied for every smooth k-algebra R, then it is also satisfied for every commutative k-algebra R.

Minor changes. Subsection 2.3 was rewritten and some references were deleted to avoid ambiguity in the definition of dg-category. Subsection 2.5 was rewritten: we only give an idea of the construction of a dg-enhancement of the derived category of perfect complexes on a scheme and provide references for the details. The proof of Theorem 3.1 (former 3.2) was shortened. 14 pages

References in corpus (4)

• The obstruction to excision in K-theory and in cyclic homology
• Isomorphism conjectures with proper coefficients
• Algebraic K-theory of Geometric Groups
• A strictly-functorial and small dg-enhancement of the derived category of perfect complexes