Pierre Deligne’s Work Algorithms

A 300-case reconstruction of Deligne’s mathematical workflow across arithmetic geometry, the Weil conjectures, weights, mixed Hodge theory, ℓ-adic sheaves, monodromy, perverse sheaves, motives, Shimura varieties, and representation theory. Each case is treated as a methodological theorem-unit: object, realization, functorial package, filtration/weight constraint, and reusable proof habit.

33 Overlapping Strategies300 CasesWeights · Sheaves · Motives · MonodromyPrevalence Histograms
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Reconstruction Method

This page is a bibliographic and methodological reconstruction, not a reproduction of Deligne’s papers. The strategy tags are overlapping: a single case may instantiate several methods, so histogram percentages indicate prevalence, not a partition of the corpus.

The reconstruction treats Deligne’s work as a repeatable sequence: replace an arithmetic or geometric problem by the right cohomological object; choose a realization; impose weights, filtrations, monodromy, or perversity; then formulate the theorem as a compatibility statement stable under functorial operations.

Object

Variety, family, sheaf, representation, motive, moduli problem, or correspondence.

Realization

Betti, de Rham, Hodge, ℓ-adic, perverse, Tannakian, or automorphic realization.

Constraint

Weight, filtration, purity, monodromy, semisimplicity, duality, or ramification.

Transfer

Trace formula, comparison theorem, functoriality, decomposition, or categorical reconstruction.

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Decision Tree of Strategies

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Prevalence Ranking

Bars show the percentage of the 300 reconstructed cases using each strategy. Since cases carry multiple tags, the total prevalence exceeds 100%.
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300-Case Corpus

#PeriodSource familyCaseMain thesis / method moveResult typeStrategy tags
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Source Spine

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Worked Demonstrations