Alexei Nikolayevich Parshin

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Alexei Parschin in Oberwolfach 2005

Alexei Nikolajewitsch Parschin ( Russian Алексей Николаевич Паршин ; mostly quoted by AN Parshin; born  November 7, 1942 in Sverdlovsk ) is a Russian mathematician who deals with number theory and algebraic geometry .

life and work

Parschin studied from 1959 at the Faculty of Mathematics and Mechanics (Mekh-Mat) of the Lomonossow University . He is currently a professor at the Steklow Institute in Moscow , where he heads the Algebra Department, and at Lomonosov University.

In 1968 Parschin showed that a finiteness presumption by Igor Schafarewitsch (which he set up at the ICM in 1962) led to the Mordell presumption . Mordell's conjecture was finally proven by Gerd Faltings in 1983 by proving the Schafarewitsch conjecture. Schafarewitsch's conjecture says that there are only a finite number of algebraic curves over an algebraic number field for a fixed gender g greater than 1 (and g = 1 with a rational point on the curve) and a given set of places of bad reduction. Schafarewitsch proved the case g = 1. In 1968, Parshin proved the Schafarewitsch conjecture for the case of functional bodies (with a technical assumption that was proven by Arakelow ) and at the same time (again) proved the Mordell conjecture in the functional body case (without using the Schafarewitsch conjecture). Parschin gave a lecture on this at the International Congress of Mathematicians (ICM) in Nice in 1970 .

He also deals with generalizations of number theoretic class field theory in higher dimensions, with integrable systems and with the history of mathematics.

He has been a correspondent since 2000 and has been a full member of the Russian Academy of Sciences since 2011 and an honorary doctorate from the University of Paris-Nord since 2001 . For the ICM 2010 he was invited to a plenary lecture ( Representations of higher adelic groups and arithmetic ). In 1970 he was invited speaker at the International Congress of Mathematicians in Nice ( Quelques conjectures de finitude en geometrie diophantienne ). In 2012 he received the Chebyshev Gold Medal from the Russian Academy of Sciences . In 2017 Parschin was elected to the Academia Europaea .

Fonts

  • AN Parshin: The way. Mathematics and Other Worlds Moscow 2002. (Russian)
  • With Schafarewitsch, he edited several volumes in the Algebraic Geometry and Number Theory series of the Encyclopedia of mathematical sciences in Springer Verlag.
  • with Schafarewitsch: The arithmetic of algebraic varieties . In: Proc. Steklov Institute Math. , 1986, No. 3.
  • with Yuri Zarhin : Finiteness problems in algebraic geometry . In: Eight papers translated from the Russian . American Mathematical Society Translations Ser.2, Volume 143, 1989, pp 35-102, revised version of the article originally published as an appendix in the Russian edition of Serge Lang Fundamentals of Diophantine Geometry , arxiv : 0912.4325
  • Parshin: Numbers as functions. The development of an idea in the Moscow school of algebraic geometry . In: Bolibruch, Osipov, Sinai (Ed.): Mathematical Events of the Twentieth Century . Springer 2006, pp. 297-330, arxiv : 0912.3785
  • Parshin: Mathematics in Moscow - it was a great epoch (PDF) In: Mitteilungen DMV , Volume 18, 2010, pp. 43–48

literature

  • Sergei Vostokov , Yuri Zarhin (Ed.): Algebraic number theory and algebraic geometry - Papers dedicated to AN Parshin on his 60th Birthday . American Mathematical Society 2002 (with foreword by Schafarewitsch)

Web links

Individual evidence

  1. ↑ previously by Yuri Manin 1963, Hans Grauert 1965
  2. ↑ Parshin: Algebraic curves over function fields 1. In: Math.USSR Izvestiya , Volume 2, 1968
  3. ↑ For example, he was involved in the Russian edition of the Collected Papers of David Hilbert and Hermann Weyl involved
personal data
SURNAME Parschin, Alexei Nikolayevich
ALTERNATIVE NAMES Parshin, Aleksey Nikolaevich; Paršin, Aleksej Nikolaevič (transliterated); Паршин, Алексей Николаевич (Russian spelling)
BRIEF DESCRIPTION Russian mathematician
DATE OF BIRTH November 7, 1942
PLACE OF BIRTH Sverdlovsk , Russian SFSR, Soviet Union