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Igor ShafarevichIgor Rostislavovich Shafarevich (Игорь Ростиславович Шафаревич: born 3 June 1923 in Zhytomyr) is a Russian mathematician, founder of the major school of algebraic number theory and algebraic geometry in the USSR. He was also an important dissident figure under the Soviet regime, a public supporter of Andrei Sakharov's Human Rights Committee from 1970. He is identified too with the criticisms of Alexandr Solzhenitsyn not only of Soviet government and communism, but also of proposed liberal ideas for the future of Russia. His work in mathematics includes the theory of the Tate-Shafarevich group (usually called 'Sha', written 'Ш', his Cyrillic initial) in Galois cohomology, and the Golod-Shafarevich theorem on class field towers. He initiated a Moscow seminar on classification of algebraic surfaces that updated around 1960 the treatment of birational geometry, and was largely responsible for the early introduction of the scheme theory approach to algebraic geometry in the Soviet school. In view of later accusations of anti-Semitism on his part, it can be noted that his research students included some identified as Jewish, and that later, during his most serious troubles in the 1970s with the Soviet authorities, he did major work in collaboration with Ilya Piatetski-Shapiro on K3 surfaces. According to a statement he released in the mid-1970s, he had had troubles with the Soviet powers in the early 1950s, but was then for a time protected by I. G. Petrovsky as Rector of Moscow University. He belonged to the wing of the dissident movement that identified itself with the Orthodox Christian tradition in Russia; what is sometimes called the 'romantic nationalist' or Slavophile tendency. The position criticised the Communist Party as part of a broader condemnation of socialism; Shafarevich published a much-noticed book Socialism (French edition around 1975) of destructive analysis, which was cited centrally by Solzhenitsyn in his 1978 address to Harvard University. From 1970 Shafarevich with Valery Chalidze, Grigori Podyapolski and Andrei Tverdokhlebov was one of Sakharov's human rights investigators. All this was a direct affront to the Soviet system, and Shafarevich was excluded from Moscow University, as was his student A. S. Tyurin. Shafarevich continued to challenge the distortions of the academic system: as reported at the time by the algebraic geometer Miles Reid, he intervened in a doctoral defence of a party placeman, bringing up questions of plagiarism and inadequate work which were simply ignored (Shafarevich as a Academician in the Soviet Academy of Sciences could expect to be heard). He wrote from this period a number of essays, on topics such as the nationalities question, 'Russophobia', Shostakovich's treatment. These were very prominent, some being included in Solzhenitsyn's collection From Under the Rubble. To be on the Sakharov committee was to invite very rough treatment. His obvious intellectual stature and personal courage, however, and his clearly professional and collegiate attitude to Jewish mathematicians as colleagues, have not always been accepted as a defence against allegations that he was personally anti-Semitic. It has been suggested that his position was somewhat isolated: it was certainly not representative of the dissidents as a whole, who included in particular some of his mathematician colleagues who were Jewish and had much less shelter from practical persecution. Shafarevich apparently subscribes to a theory that can be shortly described as a mirror-image of that of Eric Voegelin; not uncommon in itself amongst Russians. Such anti-Semitism as can really be attached to his intellectual position, rather than being anecdotal, comes from his arguing from, and interest in, the proportion of Jews in revolutionary movements. He remains a figure of controversy, and his name has become part of the small change of debates on post-Soviet Russia. External link Shafarevich Shafarevich Shafarevich Shafarevich
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