"... Formal groups. This topic is by far the deepest and most imaginative creation of Dieudonné, realized when Dieudonné was nearing 50, supposedly the term for an active mathematical life. It can be seen as the creation of a differential calculus for groups over a field of characteristic p > 0 (possibly finite). The methods of calculus do not work, and one has to resort to pure algebra. There were a number of forerunners: a version of Taylor’s formula in characteristic p > 0 due to Dieudonn ́e himself, the ideas of Delsarte about convolution operators (as explained in Book IV, chapter 6 of Bourbaki’s Éléments), a definition of the Lie algebra of a Lie group and its enveloping algebra in terms of distributions on the group (by L. Schwartz). But the impetus came from the book by Chevalley, in 1951, about algebraic groups. Chevalley had developed a purely algebraic version of Lie theory, but restricted to fields of characteristic 0. The case of characteristic p > 0 was “terra incognito”. In a long series of papers, published between 1954 and 1958, later on collected into a book ... Dieudonné explored in depth this new world."
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Pierre Cartier (mathematician)
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 was an Invited Speaker at the International Congress of Mathematicians in Nice in 1970.
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