Grothendieck: A Short Guide to His Mathematical and Philosophical Work (1949–1991)

We present a short survey of Grothendieck’s “known” work (1949–1991), before his seclusion in the Pyrenees (1991–2014). Three main periods are distinguishable: (1) 1949–1957, with his work in functional analysis, homological algebra, categories, sheaves, and K-theory; (2) 1958–1970, with the foundations of algebraic geometry, schemes, toposes, and motives; and (3) 1981–1991, with topological algebra, anabelian geometry, stacks, derivators, on the one hand, and long philosophical reflections, on the other hand.