Alexander Grothendieck
1928–2014, Berlin, Germany, Saint-Girons, France
German-born mathematician in France who rebuilt algebraic geometry on the language of schemes, sheaves, topoi, and étale cohomology, and transformed homological algebra and category theory.
Alexander Grothendieck was born in Berlin to anarchist parents; during the Second World War he was interned with his mother in France while his father perished at Auschwitz. After studying at the University of Montpellier, he went to Nancy to work under Laurent Schwartz and Jean Dieudonné, solving in less than a year a list of open problems on locally convex spaces and earning his doctorate in 1953 on topological tensor products and nuclear spaces.
Turning to algebraic geometry and homological algebra, Grothendieck published his 1957 'Tôhoku' paper placing sheaf cohomology in the setting of abelian categories and derived functors, and proved the Grothendieck–Riemann–Roch theorem using K-theory. From 1959 to 1970 at the newly founded Institut des Hautes Études Scientifiques (IHÉS), his 'Éléments de géométrie algébrique' (written with Dieudonné) and 'Séminaire de géométrie algébrique' rebuilt algebraic geometry around schemes, relative morphisms, Grothendieck topologies (sites), topoi, and étale, l-adic, and crystalline cohomology — the machinery that enabled the proof of the Weil conjectures.
Awarded the Fields Medal in 1966, Grothendieck refused to travel to Moscow in political protest; in 1970 he resigned from the IHÉS over military funding of its budget, later taught at Montpellier, declined the 1988 Crafoord Prize, and spent his last decades in seclusion in the Pyrenees.
Workplaces: Centre National de la Recherche Scientifique (CNRS), Institut des Hautes Études Scientifiques (IHÉS), University of Montpellier
France, Germany