Convergence of two obstructions for projective modules

Abstract

Let $X=SpecA$ denote a regular affine scheme, over a field $k$, with $1/2\in k$ and $\dim X=d$. Let $P$ denote a projective $A$-module of rank $n\ge 2$. Let ${\pi }_0\left(\mathcal{L}O(P)\right)$ denote the (Nori) Homotopy Obstruction set, and ${\widetilde{CH}}^n\left(X,{\Lambda }^{n}P\right)$ denote the Chow Witt group. In this article, we define a natural (set theoretic) map} $${\Theta }_P:{\pi }_0\left(\mathcal{L}O(P)\right)⟶{\widetilde{CH}}^n\left(X,{\Lambda }^{n}P\right)$$ The main Results are included in my recently published book on Algebraic $K$-Theory.

References in corpus (2)

• Hermitian K-theory, derived equivalences and Karoubi's Fundamental Theorem
• Some perspective on Homotopy obstructions