The Bousfield lattice for truncated polynomial algebras

TL;DR

This paper explores the complex structure of the derived category of a truncated polynomial ring with countably many generators, revealing a vast Bousfield lattice and constructing objects with high tensor-nilpotence height.

Contribution

It demonstrates that the Bousfield lattice for such rings is larger than the continuum and constructs objects with significant tensor-nilpotence height, advancing understanding of their derived categories.

Findings

Bousfield lattice has cardinality larger than the real numbers

Objects with large tensor-nilpotence height are constructed

Provides new insights into the structure of derived categories of truncated polynomial rings

Abstract

The global structure of the unbounded derived category of a truncated polynomial ring on countably many generators is investigated, via its Bousfield lattice. The Bousfield lattice is shown to have cardinality larger than that of the real numbers, and objects with large tensor-nilpotence height are constructed.