Solutions to all three questions of the Introduction to schemes course of the University of Oxford, Part C, sat on 1 June 2021. Source: Oxford's released examination PDF, compilation pages 103–106; paper pages 1–4. The original question and letter labels are retained; the paper has no Roman subparts. The correction to the printed closed-subset description in 1(b), and the meaning of the comparison of structure sheaves in 1(c), are explained where they arise.
Solutions to all three questions of the Introduction to schemes course of the University of Oxford, Part C, sat on 8 June 2023. Source: Oxford's released examination PDF, compilation pages 346–348; paper pages 1–3. The original numeric, letter and Roman labels are retained. The compactness hypotheses in the valuative criterion and the interpretation of the removed section in 3(e) are made explicit below.