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He attended the International Congress of Mathematicians in August 1966 held in Moscow and accepted Alexander Grothendieck's Fields Medal on his behalf as Grothendieck boycotted the Congress to protest over the treatment of the dissident writers.
During 1964-1967 at the Forschungsinstitut für Mathematik at the ETH in Zurich he worked on the Category of Categories and was especially influenced by Pierre Gabriel's seminars at Oberwolfach on Grothendieck's foundation of algebraic geometry.
In his thesis, Messing elaborated on Grothendieck's 1970 lecture at the International Congress of Mathematicians in Nice on p-divisible groups (Barsotti–Tate groups) that are important in algebraic geometry in prime characteristic, which were introduced in the 1950s by Dieudonné in his study of Lie algebras over fields of finite characteristic.