Year: 2018
Type: preprint
Abstract: Throughout $A$ will denote commutative noetherian ring, with $\dim A=d\geq 2$, and $P$ denote a projective $A$-module with $rank(P)=n$. In \cite{MM1} we considered the Homotopy obstruction sets $π_0\left({\mathcal LO}(P)\right)$, which has a structure of an abelian monoid, under suitable regularity and other conditions. In this article, we provide some perspective on these sets $π_0\left({\mathcal LO}(P)\right)$. Under similar regularity and other conditions, we prove if $P, Q$ are two projective $A$-modules, with $rank(P)=rank(Q)=d$ and $\det(P) \cong \det Q$, then $π_0\left({\mathcal LO}(Q)\right)\cong π_0\left({\mathcal LO}(P)\right)$. Further, for any projective $A$-module $P$ with $rank(P)=n$, we define a natural set theoretic map $π_0\left({\mathcal LO}(P)\right)\rightarrow CH^n(A)$, where $CH^n(A)$ Chow groups of codimension $n$ cycles.
Source: arXiv (Cornell University)
Authors: Mandal, Satya, Mishra, Bibekananda
Institution: University of Kansas
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2900249398