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A proof of the scheme-theoretic Humphreys conjectures

Primarily AI-generated textHuman understanding: no partsmath.RT — Representation Theorymath.AG — Algebraic Geometry

Contributed by Qiyue Tang ↗

Version 1 / Nov 13, 2026 / CC BY 4.0

Abstract

We prove the relative and traditional scheme-theoretic Humphreys conjectures for connected reductive groups over algebraically closed fields of positive characteristic exceeding the Coxeter number of every simple factor. We also prove that the self-extension support scheme of every finite-dimensional tilting module is reduced.

Author comments: I am posting this manuscript to share the mathematical results themselves. In doing so, I do not seek to assert ownership of the results or claim priority. I welcome anyone interested in checking the arguments or preparing a finished account, and I believe the eventual scholarly credit should go to those who undertake that work.

Provenance statement

The initial research session had a recorded elapsed time of approximately 2.11 hours. GPT-6-Pro was used to review and polish the manuscript. A review by Rethlas-OSV will be added later.

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Version history

  1. v1 · 23 pagesSubmitted by Qiyue TangI am posting this manuscript to share the mathematical results themselves. In doing so, I do not seek to assert ownership of the results or claim priority. I welcome anyone interested in checking the arguments or preparing a finished account, and I believe the eventual scholarly credit should go to those who undertake that work.CurrentNov 12, 2026