Bernhard Köck

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Using Quillen’s universal transformation we verify some (standard) properties of Adams operations on the higher K -theory of projective modules over group rings. Furthermore, we rather explicitly describe Adams operations on the Whitehead group K1(CΓ ) associated with the group ring CΓ of a finite group Γ over an algebraically closed field of characteristic(More)
Let Γ be a finite group and K a number field. We show that the operation ψk defined by Cassou-Noguès and Taylor on the locally free classgroup Cl(OKΓ ) is a symmetric power operation if gcd(k, ord(Γ )) = 1. Using the equivariant Adams-Riemann-Roch theorem, we furthermore give a geometric interpretation of a formula established by Burns and Chinburg for(More)
Let R be a commutative ring and I an ideal in R which is locally generated by a regular sequence of length d. Then, each f. g. projective R/I-module V has an Rprojective resolution P. of length d. In this paper, we compute the homology of the n-th Koszul complex associated with the homomorphism P1 → P0 for all n ≥ 1, if d = 1. This computation yields a new(More)
We prove a certain Riemann-Roch type formula for symmetric powers of Galois modules on Dedekind schemes which, in the number field or function field case, specializes to a formula of Burns and Chinburg for Cassou-Noguès-Taylor operations. Introduction Let G be a finite group and E a number field. Let OE denote the ring of integers in E, Y := Spec(OE), and(More)
Let R be a commutative ring, Γ a group acting on R , and let k ∈ IN be invertible in R . Generalizing a definition of Kervaire we construct an Adams operation ψ on the Grothendieck group and on the higher K theory of projective modules over the twisted group ring R#Γ . For this we use generalizations of Atiyah’s cyclic power operations and shuffle products(More)