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.
He was awarded the Prize Ampère of the French Academy of Sciences in 1979.
In 2012 he became a fellow of the American Mathematical Society.