On Chow groups of toric schemes over a DVR

TL;DR

This paper provides an explicit combinatorial description of the Chow groups of toric schemes over a DVR, enabling computations for various schemes and their special fibers.

Contribution

It introduces a new combinatorial framework for understanding Chow groups of toric schemes over a DVR, including explicit calculations.

Findings

Explicit combinatorial presentation of Chow groups

Computed Chow groups for several toric schemes over a DVR

Analyzed Chow groups of special fibers

Abstract

We give an explicit combinatorial presentation of the Chow groups of a toric scheme over a DVR. As an application, we compute the Chow groups of several toric schemes over a DVR and of their special fibers.