On components of stable Auslander-Reiten quivers that contain Heller lattices: the case of truncated polynomial rings

Abstract

Let $A$ be a truncated polynomial ring over a complete discrete valuation ring $\mathcal{O}$, and we consider the additive category consisting of $A$-lattices $M$ with the property that $M\otimes \mathcal{K}$ is projective as an $A\otimes \mathcal{K}$-module, where $\mathcal{K}$ is the fraction field of $\mathcal{O}$. Then, we may define the stable Auslander-Reiten quiver of the category. We determine the shape of the components of the stable Auslander-Reiten quiver that contain Heller lattices.

arXiv comment29 pages (v2) typo corrected (v3) several errors corrected (v4) modified some parts in subsections 1.3, 1.4 and 1.5