Pierre Cartier was a member of the Bourbaki, and a friend and colleague of Alexander Grothendieck. He is known for the eponymous Cartier divisor and the introduction of the Cartier operator in algebraic geometry in characteristic p, as well as for his work on duality of abelian varieties and formal groups. He was awarded the Ampère Prize of the French Academy of Sciences. He is a fellow of the American Mathematical Society.