This thesis, under Grothendieck, was defended on July 3, 1969, at IHP (Paris), in front of a jury chaired by P. Samuel, with examiners J. Dixmier, A. Grothendieck, and J. L. Verdier.
An important precursor to the thesis was the Seminar SGA5 (1965/66), during which J. P. Jouanolou delivered three consecutive exposés. These exposés elaborated on key concepts and techniques that would directly influence his own thesis work. In Exposé III Intro, we find the following statement:
“Faute de disposer d’une bonne catégorie dérivée de faisceaux ℓ-adiques (la thèse de Jouanolou n’ayant malheureusement pas été publiée), nous travaillons systématiquement avec des coefficients de torsion (première aux caractéristiques résiduelles).”
The thesis holds significant historical value as it reflects, in some sense, a language and an approach developed during Grothendieck’s active years. In the 1980s, he wrote in “Récoltes et Semailles”:
“De toutes façons, c’est aujourd’hui encore le seul texte au monde qui présente la théorie des coefficients ℓ-adiques, version catégories dérivées — et un texte introuvable par dessus le marché, pour mettre la joie à son comble.”
This project, involving the transcription of J.-P. Jouanolou’s thesis, was conducted with his authorization. It was typeset in LATEX under the direction of Mateo Carmona, with the collaboration of Niels Borne, along with volunteers:
- Bruno Kahn
- Fan Xuanrui
The transcription aims to be as faithful as possible to the original. Its edition is considered provisional, and we welcome any remarks, comments, and corrections.
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