Rational algebraic $K$-theory of certain truncated polynomial rings

Algebraic K-theory of Monoid Rings

Are all finitely generated projective k[t1, . . . , td]-modules free for an arbitrary field k and arbitrary d ∈ N? This question, set in Serre’s famous paper FAC in 1955, inspired an enormous activity of algebraists worldwide. The activity culminated in two independent confirmations of the question in 1976 by Quillen and Suslin. In the meanwhile the algebraic K-theory was created, in which one ...

Algebraic and Hermitian K-theory of K-rings

The main purpose of the present article is to establish the real case of “Karoubi’s Conjecture” [20] in algebraic K-theory. The complex case was proved in 1990-91 (cf. [32] for the C∗-algebraic form of the conjecture, and [38] for both the Banach and C∗-algebraic forms). Compared to the case of complex algebras, the real case poses additional difficulties. This is due to the fact that topologic...

Determinantal Varieties over Truncated Polynomial Rings

We study higher order determinantal varieties obtained by considering generic m × n (m ≤ n) matrices over rings of the form F [t]/(t k), and for some fixed r, setting the coefficients of powers of t of all r × r minors to zero. These varieties can be interpreted as generalized tangent bundles over the classical deter-minantal varieties; a special case of these varieties first appeared in a prob...

Lower Algebraic K-theory of Certain Reflection Groups

For P ⊂ H3 a finite volume geodesic polyhedron, with the property that all interior angles between incident faces are of the form π/mij (mij ≥ 2 an integer), there is a naturally associated Coxeter group ΓP . Furthermore, this Coxeter group is a lattice inside the semi-simple Lie group O+(3, 1) = Isom(H3), with fundamental domain the original polyhedron P . In this paper, we provide a procedure...

Differential Polynomial Rings of Triangular Matrix Rings