Pierre Émile Cartier (born 10 June 1932) is a French mathematician. An associate of the Bourbaki group and at one time a colleague of Alexander Grothendieck, his interests have ranged over algebraic geometry, representation theory, mathematical physics, and category theory.

He studied at the École Normale Supérieure in Paris under Henri Cartan and André Weil.^[2] Since his 1958 thesis on algebraic geometry he has worked in a number of fields. He is known for the introduction of the Cartier operator in algebraic geometry in characteristic p, and for work on duality of abelian varieties and on formal groups. He is the eponym of Cartier divisors and Cartier duality.

From 1961 to 1971 he was a professor at the University of Strasbourg. In 1970 he was an Invited Speaker at the International Congress of Mathematicians in Nice.^[3] He was awarded the 1978 Prize Ampère of the French Academy of Sciences.^[4] In 2012 he became a fellow of the American Mathematical Society.^[5]

• Cartier, Pierre; Foata, Dominique (14 November 2006). Problèmes combinatoires de commutation et réarrangements. Springer. ISBN 9783540360940. (1st edition 1969)^[6]
• Waldschmidt, Michel; Moussa, Pierre; Luck, Jean-Marc; Itzykson, Claude, eds. (9 March 2013). "An introduction to zeta functions by Pierre Cartier". From Number Theory to Physics. Springer. pp. 1–63. ISBN 9783662028384. (1st edition 1992)
• "A primer of Hopf algebras" (PDF). Report Number IHES-M-2006-40: 1–74. September 2006.
• Freedom in Mathematics, Springer India, 2016 (with Cédric Villani, Jean Dhombres, Gerhard Heinzmann), ISBN 978-81-322-2786-1.^[7]
  • Translation from the French language edition: Mathématiques en liberté, La Ville Brûle, Montreuil 2012, ISBN 978-23-601-2026-0.
• Pierre Cartier: Alexander Grothendieck. A country known only by name. Notices AMS, vol. 62, 2015, no. 4, pp. 373–382, PDF.

• Cotangent complex
• Dieudonné module
• MacMahon's master theorem