Search

This paper uses differential-graded methods to give a streamlined proof of a theorem of Foxby-Halvorson. The theorem states that certain relative K-groups made from complexes with bounded (but arbitrarily long) length coincide with similar K-groups in which one sets an absolute bound on the length of the complexes.

We give a negative answer to the question raised by Mart Abel about whether his proposed definition of ${K}_{0} $ and ${K}_{1} $ groups in terms of quasi multiplication is indeed equivalent to the established ones in algebraic $K$-theory.

Let G be a finite group. To a set of subgroups of order two we associate a mod 2 Hecke algebra and construct a homomorphism, ψ, from its units to the class-group of Z[G]. We show that this homomorphism takes values in the subgroup, D(Z[G]). Alternative constructions of Chinburg invariants arising fromthe Galois module structure of higher-dimensional algebraic K-groups of rings of algebraic integers often differ by elements in the image of ψ. As an application we show that two such constructions coincide.

Search Results

Refine search

Refine search

Actions for selected content:

3 results

Grothendieck groups of complexes with null-homotopies

QUASI MULTIPLICATION AND $K$-GROUPS

Hecke Algebras and Class-Group Invariants

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

3 results

Grothendieck groups of complexes with null-homotopies

QUASI MULTIPLICATION AND $K$-GROUPS

Hecke Algebras and Class-Group Invariants