Grothendieck, Alexander Grothendieck School, École Normale Supérieure, University of Montpellier, Bourbaki, Étale cohomology, Scheme theory, Homological algebra, Motives, Grothendieck-Riemann-Roch theorem, Anabelian geometry, Category theory, Connes, Alain

Alexander Grothendieck was a pioneering mathematician known for revolutionizing algebraic geometry. His school and associations, like the École Normale Supérieure and University of Montpellier, fostered advanced research. He was connected to the Bourbaki group, which aimed to reformulate mathematics fundamentally. Key concepts such as étale cohomology, scheme theory, and motives developed under his influence, expanding understanding of geometric structures. Major contributions include the Grothendieck-Riemann-Roch theorem and advances in homological algebra and category theory, which underpin modern mathematics. Collaborator Alain Connes advanced noncommutative geometry, relating to Grothendieck’s work. Overall, his ideas shape contemporary geometric and algebraic research.