[Article title missing]

Abstract

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.

Keywords

• Infinitesimal neighborhood
• de Rham complex
• de Rham cohomology
• crystalline cohomology
• $p$-adic Hodge theory
• cotangent complex
• prismatic cohomology