Finite homological dimension and a derived equivalence

For a Cohen-Macaulay ring $R$, we exhibit the equivalence of the bounded derived categories of certain resolving subcategories, which, amongst other results, yields an equivalence of the bounded derived category of finite length and finite projective dimension modules with the bounded derived category of projective modules with finite length homologies. This yields isomorphisms of various generalized cohomology groups (like K-theory) and improves on terms of a spectral sequence and Gersten complexes.Comment: 23 pages : Some parts of the article changed, especially section 3, to add clarity. Other minor corrections mad

Transglutaminase 2 at the Crossroads between Cell Death and Survival

n/

Projective modules over smooth, affine varieties over Archimedean real closed fields

Let X = Spec(A) be a smooth, affine variety of dimension n ≥ 2 over the field of R real numbers. Let P be a projective A-module of such that its nth Chern class Cn(P) ∈ CH0(X) is zero. In this set-up, Bhatwadekar-Das-Mandal showed (amongst many other results) that P A⊕Q in the case that either n is odd or the topological space X(R) of real points of X does not have a compact, connected component. In this paper, we prove that similar results hold for smooth, affine varieties over an Archimedean real closed field R