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Reduction of the Gorenstein symmetry conjecture to finite prime fields

A mix of human-written and AI-generated textHuman understanding: some partsmath.RT — Representation Theory

Contributed by Qiyue Tang ↗

Version 1 / Oct 20, 2026 / CC BY 4.0

Abstract

We prove that the Gorenstein symmetry conjecture for finite-dimensional algebras over arbitrary fields is equivalent to its restriction to the finite prime fields. A counterexample specializes to a finite field without changing its dimension or its finite self-injective dimension. In characteristic zero, a counterexample yields counterexamples of one fixed dimension over every prime field outside a finite set.

Provenance statement

Some of the results in this paper were obtained by AI.

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Version history

  1. v1Submitted by Qiyue TangInitial depositCurrentOct 19, 2026