Research-page premise
Grothendieck's work repeatedly changes the arena before solving the problem: from spaces to functors, from varieties to schemes, from points to topoi, from examples to universal properties, from theorems to foundations, and from isolated proofs to seminar-scale infrastructures.
Methodological rule: later vocabulary is used as retrospective labeling only. The reconstruction does not assume mathematical developments after Grothendieck's active period as premises for his own derivations.
Thirty-three reconstructed strategies
Select a strategy
Click a card above to see its inferred use, formula cue, and case evidence.
Overlapping prevalence ranking
Because each case may use several strategies, the percentages below are prevalence rates: count divided by 300 cases. They are not normalized to sum to 100%.
300 publication / chapter / exposé cases
| # | Year | Case / lecture title | Source | Thesis/result abstraction | Strategies |
|---|
Worked demonstrations
Source spine and limitation
This page is a bibliographic and methodological reconstruction. It uses public publication lists, EGA/SGA/FGA tables and archive descriptions, and known programmatic manuscripts as the spine. It does not reproduce copyrighted full text, and it distinguishes exact bibliographic identity from inferred strategy labels.