Mixed Motives over $k[t]/{(t^{m+1})}$

TL;DR

This paper constructs a triangulated category of mixed motives over a specific algebraic structure, linking Ext groups to higher Chow groups and additive higher Chow groups, advancing the understanding of motives over truncated polynomial rings.

Contribution

It introduces a new triangulated category of mixed motives over $k[t]/(t^{m+1})$, connecting Ext groups with higher and additive higher Chow groups.

Findings

Ext groups correspond to higher Chow groups

Ext groups also relate to additive higher Chow groups

Provides a framework for motives over truncated polynomial rings

Abstract

For a perfect field $k$, we construct a triangulated category of mixed motives over $k[t]/{(t^{m+1})}$. The ext groups in this category are given by higher Chow groups, and additive higher Chow groups.