Igor Shafarevich

Igor Rostislavovich Shafarevich, who lived from 3 June 1923 to 19 February 2017, was a Soviet and Russian mathematician who contributed to algebraic number theory and algebraic geometry. He made early contributions to explicit formulas for the Hilbert pairing, proved that every finite solvable group is a Galois group over the rationals, shared the Golod-Shafarevich theorem on towers of unramified extensions, and with John Tate introduced the group now called the Tate-Shafarevich group. He led a Moscow seminar on the classification of algebraic surfaces and helped bring scheme theory into Soviet algebraic geometry. His conjecture on finiteness of abelian varieties with fixed bad reduction was proved by Gerd Faltings on the way to the Mordell conjecture. His students included Yuri Manin, Aleksei Parshin, Igor Dolgachev and Suren Arakelov. He was a foreign member of the Royal Society from 1981, and outside mathematics wrote on politics and religion, including The Socialist Phenomenon.