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AI-assisted counterexample to Grothendieck’s group-scheme question

Akhil Mathew’s contribution gives a noncommutative finite free group scheme of order four over a nonreduced base that is not killed by four.

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Understanding the problem

Read the background

Akhil Mathew’s contribution gives a noncommutative finite free group scheme of order four over a nonreduced base that is not killed by four.

Why it matters

If correct, refutes a longstanding general group-scheme assertion with an explicit order-four example, retaining the known positive cases.

What counts as progress

A sourced result with the exact hypotheses, baseline, and AI role stated; verification is assessed separately.

What to watch for

  • Compare the precise theorem and hypotheses with the previous baseline.
  • Read the checking scope and retain human and prior-work attribution.

Background review: 2026-10-11. Selected sources:

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