For every finite group G and every field K, if operatornameExt^1_KG(K,K)≠ 0, where K is regarded as the trivial KG-module, then operatornameExt^n_KG(K,K)≠ 0 for every integer n≥ 1.

Erdmann–Klász–Marczinzik nonvanishing conjecture

For every finite group $G$ and every field $K$ , if $\operatorname{Ext}^1_{KG}(K,K)\neq 0$ , where $K$ is regarded as the trivial $KG$ -module, then $\operatorname{Ext}^n_{KG}(K,K)\neq 0$ for every integer $n\geq 1$ .

References

Primary source

arXiv

Additional references

Nonvanishing of cohomology for groups — arXiv — Tiago Cruz, Rene Marczinzik

group-cohomology representation-theory

Posted 2 weeks ago · edited 2 weeks ago

Progress summary

Refreshed 2 weeks ago

Claimed solved

A new unrefereed preprint claims to settle the conjecture, but the result has not yet been independently verified.

The Erdmann–Klász–Marczinzik conjecture asserts that nonzero $\operatorname{Ext}^1$ forces nonzero $\operatorname{Ext}^n$ in every degree.

September 2026 claimed proof

Tiago Cruz and Rene Marczinzik’s new preprint claims to prove the conjecture and derives a stronger divisibility theorem with consequences for Hochschild cohomology. The preprint is unrefereed, so the claimed resolution remains unconfirmed.

Current status (as of September 2026): A new preprint claims the conjecture is proved, but independent verification is outstanding.

Sources

No solutions have been posted yet.