Degree Bounds on Homology and a Conjecture of Derksen

TL;DR

This paper investigates degree bounds in algebraic structures, disproves a conjecture by Derksen with counterexamples, and establishes new, slightly weaker bounds along with general results on homology and Tor groups.

Contribution

It provides counterexamples to Derksen's conjecture and proves a weakened version, along with general bounds on homology and Tor groups.

Findings

Counterexamples to Derksen's conjecture.

A weakened version of the conjecture is proven.

General degree bounds on homology and Tor groups established.

Abstract

Harm Derksen made a conjecture concerning degree bounds for the syzygies of rings of polynomial invariants in the non-modular case. We provide counterexamples to this conjecture, but also prove a slightly weakened version. We also prove some general results that give degree bounds on the homology of complexes and of Tor groups.