A. Grothendieck's early work (1950-1960) (Q910382)

The author discusses the contribution of Alexander Grothendieck to functional analysis beginning with his investigation of the theory of locally convex spaces around 1950 and his doctoral dissertation in 1953. Brief details of his stay at Kansas University in 1955 during which he worked on homological algebra and holomorphic vector bundles is included but most of the paper is devoted, in some detail, to the latter half of the decade and early 1960's. Above all the development of Grothendieck topologies as a tool towards cohomologies with coefficients in a field of characteristic zero is considered his ultimate achievement.