Igor Shafarevich (nonfiction)

Igor Rostislavovich Shafarevich.

Igor Rostislavovich Shafarevich (Russian: И́горь Ростисла́вович Шафаре́вич; 3 June 1923 – 19 February 2017) was a Russian mathematician who contributed to algebraic number theory and algebraic geometry.

Shafarevich made fundamental contributions to several parts of mathematics including algebraic number theory, algebraic geometry and arithmetic algebraic geometry. In algebraic number theory the Shafarevich–Weil theorem extends the commutative reciprocity map to the case of Galois groups which are extensions of abelian groups by finite groups. Shafarevich was the first to give a completely self-contained formula for the pairing which coincides with the wild Hilbert symbol on local fields, thus initiating an important branch of the study of explicit formulas in number theory. Another famous result is Shafarevich's theorem on solvable Galois groups giving the realization of every finite solvable group as a Galois group over the rationals. Another fundamental result is the Golod–Shafarevich theorem on towers of unramified extensions of number fields.

Shafarevich and his school greatly contributed to the study of algebraic geometry of surfaces. 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. His investigation in arithmetic of elliptic curves led him independently of John Tate to the introduction of the most mysterious group related to elliptic curves over number fields, the Tate–Shafarevich group (usually called 'Sha', written 'Ш', his Cyrillic initial). He introduced the Grothendieck–Ogg–Shafarevich formula and the Néron–Ogg–Shafarevich criterion. He also formulated the Shafarevich conjecture which stated the finiteness of the set of Abelian varieties over a number field having fixed dimension and prescribed set of primes of bad reduction. This conjecture was proved by Gerd Faltings as a step in his proof of the Mordell conjecture.

He wrote books and articles that criticize socialism, and was an important dissident during the Soviet regime.

Shafarevich came into conflict with the Soviet authorities in the early 1950s, but was protected by Ivan Petrovsky, the Rector of Moscow University. He belonged to a group of Pochvennichestvo-influenced dissidents who endorsed the Orthodox Christian tradition.

Shafarevich published a book, The Socialist Phenomenon (French edition 1975 English edition 1980), which was cited by Solzhenitsyn in his 1978 address to Harvard University.

In the 1970s Shafarevich, with Valery Chalidze, Grigori Podyapolski and Andrei Tverdokhlebov, became one of Sakharov's human rights investigators, and was consequently dismissed from Moscow University.

Nonfiction cross-reference

• Mathematics (nonfiction)

External links:

• Igor Shafarevich @ Wikipedia