Grothendieck and differential calculus

Luc Illusie

doi:10.5802/crmath.764

Historical Commentary - Algebra

Grothendieck and differential calculus

Luc Illusie ¹

¹ Institut de Mathématique d’Orsay, Bât. 307, Université Paris-Saclay, 91405 Orsay Cédex, France

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 829-841

Abstract (Original language)
Résumé

I discuss some of the contributions that Grothendieck brought to differential calculus in the 1960s (infinitesimal neighborhoods, algebraic de Rham cohomology, crystalline cohomology) and sketch a few recent developments.

Je présente quelques-unes des contributions que Grothendieck a apportées au calcul différentiel dans les années 1960 (voisinages infinitésimaux, cohomologie de de Rham algébrique, cohomologie cristalline), et esquisse certains développements récents.

Received: 2025-02-11
Accepted: 2025-06-06
Revised after acceptance: 2025-06-12
Published online: 2025-07-15

DOI: 10.5802/crmath.764

Classification: 14F20, 14F30, 14F40
Keywords: Infinitesimal neighborhood, de Rham complex, de Rham cohomology, crystalline cohomology, $p$-adic Hodge theory, cotangent complex, prismatic cohomology
Mots-clés : Voisinage infinitésimal, complexe de de Rham, cohomologie de de Rham, cohomologie cristalline, théorie de Hodge $p$-adique, complexe cotangent, cohomologie prismatique

Author's affiliations:

Luc Illusie ¹

¹ Institut de Mathématique d’Orsay, Bât. 307, Université Paris-Saclay, 91405 Orsay Cédex, France

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Luc Illusie. Grothendieck and differential calculus. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 829-841. doi: 10.5802/crmath.764

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