Igor Shafarevich | |
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| Born | Igor Rostislavovich Shafarevich (1923-06-03)3 June 1923[1] |
| Died | 19 February 2017(2017-02-19) (aged 93) Moscow, Russia |
| Alma mater | Steklov Institute of Mathematics |
| Known for | Shafarevich–Weil theorem,Golod–Shafarevich theorem,Shafarevich's theorem on solvable Galois groups,Grothendieck–Ogg–Shafarevich formula,Néron–Ogg–Shafarevich criterion |
| Awards | Leonard Euler Gold Medal(2017) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Lomonosov Moscow State University |
| Doctoral advisor | Boris Delaunay |
| Doctoral students | |
Igor Rostislavovich Shafarevich (Russian:И́горь Ростисла́вович Шафаре́вич; 3 June 1923 – 19 February 2017) was aSoviet andRussianmathematician who contributed toalgebraic number theory andalgebraic geometry. Outside mathematics, he wrote books and articles that criticisedsocialism and other books which were described asanti-semitic.
From his early years, Shafarevich made fundamental contributions to several parts ofmathematicsincludingalgebraic number theory,algebraic geometry andarithmetic algebraic geometry. In particular, in algebraic number theory, theShafarevich–Weil theorem extends the commutative reciprocity map to the case ofGalois groups, which are central extensions ofabelian groups byfinite groups.
Shafarevich was the first mathematician to give a completely self-contained formula for the Hilbert pairing, thus initiating an important branch of the study of explicit formulas innumber theory. Another famous (and slightly incomplete) result isShafarevich's theorem on solvable Galois groups, giving the realization of every finitesolvable group as a Galois group over therationals.
Another development is theGolod–Shafarevich theorem on towers ofunramified extensions ofnumber fields.
Shafarevich and his school greatly contributed to the study of algebraic geometry ofsurfaces. He started a famousMoscow seminar onclassification of algebraic surfaces that updated the treatment ofbirational geometry around 1960 and was largely responsible for the early introduction of thescheme theory approach to algebraic geometry in the Soviet school. His investigation in arithmetic ofelliptic curves led him, independently ofJohn Tate, to the introduction of the group related toelliptic curves over number fields, theTate–Shafarevich group (usually called 'Sha', and denoted as 'Ш', the firstCyrillic letter of his surname).
He contributed theGrothendieck–Ogg–Shafarevich formula and to theNéron–Ogg–Shafarevich criterion.
With former studentIlya Piatetski-Shapiro, he proved a version of theTorelli theorem forK3 surfaces.
He formulated theShafarevich conjecture, which stated the finiteness of the set ofAbelian varieties over a number field having fixed dimension and prescribed set of primes ofbad reduction. The conjecture was proved byGerd Faltings as a partial step in his proof of theMordell conjecture.
Shafarevich's students includedYuri Manin,Alexey Parshin,Igor Dolgachev,Evgeny Golod,Alexei Kostrikin,Suren Arakelov,G. V. Belyi, Victor Abrashkin, Andrey Todorov, Andrey N. Tyurin, andVictor Kolyvagin.
He was a member of theSerbian Academy of Sciences and Arts in the department of Mathematics, Physics and Earth Sciences.In 1960, he was elected a Member of theGerman Academy of Sciences Leopoldina.[2] In 1981, he was elected as a foreign member of theRoyal Society.[3]
In 2017, Shafarevich was awarded theLeonhard Euler Gold Medal by theRussian Academy of Sciences.
Shafarevich came into conflict with the Soviet authorities in the early 1950s but was protected byIvan Petrovsky, the Rector ofMoscow University. He belonged to a group ofPochvennichestvo-influenced dissidents who endorsed theEastern Orthodox tradition. Shafarevich published a book,The Socialist Phenomenon (French edition 1975, English edition 1980), which was cited byAleksandr Solzhenitsyn in his 1978 address toHarvard University.
In the 1970s, Shafarevich, withValery Chalidze,Grigori Podyapolski andAndrei Tverdokhlebov, became one ofAndrei Sakharov'shuman rights investigators and so was dismissed from Moscow University. Shafarevich opposed political interference in universities.
Shafarevich's bookThe Socialist Phenomenon,[4] which was published in theUS byHarper & Row in 1980, analyzed numerous examples of socialism from ancient times to various medieval heresies and a variety of modern thinkers and socialist states. From those examples, he claimed that all the basic principles of socialist ideology derive from the urge to suppressindividualism.The Socialist Phenomenon consists of three major parts:[5]
Shafarevich argued that ancient socialism (such as Mesopotamia and Egypt) was not ideological, as an ideology socialism was a reaction to the emergence of individualism in theAxial Age. He comparedThomas More's (Utopia) andTommaso Campanella's (City of the Sun) visions with what is known about theInca Empire and concluded that there are striking similarities. He claimed that we become persons through our relationship with God and argued that socialism is essentiallynihilistic and is unconsciously motivated by a death instinct. He concluded that we have the choice of pursuing death or life.
Shafarevich adhered toRussian Orthodox Christianity and incorporated theneo-Platonic views ofEastern Orthodoxy into his understanding of the relation of mathematics and religion.[9]
In his talk to theGöttingen Academy of Sciences upon receiving a prize, Shafarevich presented his view of the relationship between mathematics and religion. He noted the multiple discoveries in mathematics, such as that ofnon-Euclidean geometry, to suggest that pure mathematics reflects an objective reality, not a set of conventional definitions or a formalism. He claimed that the growth of mathematics itself is not directed or organic. To have a unity and direction, mathematics needs a goal. It can be practical applications or God as the source for the direction of development. Shafarevich opted for the latter, as pure mathematics is not in itself driven by practical applications.[10]
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On 21 December 1991 he took part in the first congress of theRussian All-People's Union, headed bySergei Baburin. In October 1992, he became a member of the founding committee of theNational Salvation Front. In 1993, he was an unsuccessful candidate for theState Duma withMikhail Astafyev'sConstitutional Democratic Party - Party of Popular Freedom.
Shafarevich was a member of the editorial board of the magazineNash Sovremennik and in 1991–1992 of the editorial board ofDen ofAlexander Prokhanov, which was banned in October 1993 following the1993 Russian constitutional crisis and later reopened under the titleZavtra. In 1994, he joined the "All-Russian National Right Wing Centre", led byMikhail Astafyev.
Shafarevich's essayRussophobia[11] was expanded into his bookThree Thousand-Year-Old Mystery (Трехтысячелетняя загадка) and resulted in accusations ofantisemitism.[12][13][14] He completed theRussophobia essay in 1982 and it was initially circulated assamizdat. In the Soviet Union, it was first officially published in 1989. At the same time, Shafarevich condemned the methods that were used toscreen out applicants of Jewish origin when entering prestigious Moscow universities in the 1970s and early 1980s.[15]
InRussophobia, he argued in the essay that great nations experience periods in their history of reformist elitist groups ('small nations') having values that differ fundamentally from the values of the majority of the people but gaining the upper hand in the society. In Shafarevich's opinion, the role of such a 'small nation' in Russia was played by a small group ofintelligentsiya, dominated byJews, "who were full of hatred against traditional Russian way of life and played an active role in the terrorist regimes ofVladimir Lenin andJoseph Stalin".[16][17]
Its publication led to a request by theUnited States National Academy of Sciences (NAS) to Shafarevich to resign his membership,[18] because the NAS charter prohibited stripping an existing membership.[19][20] In an open letter to the NAS, Shafarevich explained thatRussophobia is not antisemitic.[21] Shafarevich also noted that since NAS enlisted him without his request or knowledge, delisting him was its internal matter. Nevertheless, when the United Statesinvaded Iraq, Shafarevich faxed his resignation.[22]
Accusations of antisemitism continued and involved Shafarevich's other publications.[23]Semyon Reznik targets theRussophobia essay for factual inaccuracies: Shafarevich misassigned Jewish ethnicity to a number of non-Jews involved in the execution ofNicholas II, repeated the false assertion of graffiti inYiddish at the murder site and suggested that Shafarevich's phrase "Nicholas II wasshot specifically as theTsar, and this ritual act drew a line under an epoch in Russian history" – is read by some as ablood libel.[16] (An accusation which ignores the remainder of Shafarevich's sentence: "so it can only be compared with the execution of Charles I in England or of Louis XVI in France".)[11]Aron Katsenelinboigen wrote that Shafarevish's work "lives up to the best traditions of antisemitic propaganda".[24]
Later, Shafarevich expanded on his views in his bookThree Thousand-Year-Old Mystery in which he further claimed that Jews effectively marginalise and exclude non-Jews in all types of intellectual endeavors. The work was published in Russian in 2002; an introductory section explains the relationship with theRussophobia essay, explaining that the essay developed from an appendix to an intended work of wider scope, which he started writing insamizdat.[25]
In 2005, Shafarevich was amongst the signatories of theLetter of 5000.
The issue of Shafarevich's alleged antisemitism has been the subject of a 2009 doctoral thesis at theUniversity of Helsinki, which was later turned into a book[1] in which the author, Krista Berglund, stated that Shafarevich's views have been misconstrued as antisemitic.[26]
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