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Aleksei N. Parshin
Алексей Николаевич Паршин
Alexei Parshin.jpg
Aleksei Parshin in Oberwolfach 2005
Born(1942-11-07)7 November 1942
Died18 June 2022(2022-06-18) (aged 79)
NationalityRussian
Alma materSteklov Institute of Mathematics
Known for
Awards
Scientific career
FieldsMathematics
Institutions
Doctoral advisorIgor Shafarevich
Aleksei Nikolaevich Parshin (Russian: Алексей Николаевич Паршин; 7 November 1942 – 18 June 2022) was a Russian mathematician, specializing in arithmetic geometry. He is most well-known for his role in the proof of the Mordell conjecture.
Contents
1 Biography
2 Awards and honors
3 Selected publications
4 Sources
5 See also
6 Notes
7 References
8 External links
Biography
Parshin was born on 7 November 1942. He graduated in 1964 from the Faculty of Mathematics and Mechanics of Moscow State University and then enrolled as a graduate student at the Steklov Institute of Mathematics, where he received his Kand. Nauk (Ph.D.) in 1968 under Igor Shafarevich. In 1983 he received his Doctor Nauk (doctorate of sciences) from Moscow State University. He was a professor at the Steklov Institute of Mathematics in Moscow, where he was the head of the Department of Algebra. He was also a professor at Moscow State University.
In 1968, Parshin proved that the Mordell conjecture is a logical consequence of Shafarevich's finiteness conjecture concerning isomorphism classes of abelian varieties via what is known as Parshin's trick, which gives an embedding of an algebraic curve into the Siegel modular variety. In 1983 Gerd Faltings proved Shafarevich's finiteness conjecture (and thereby the Mordell conjecture).
Shafarevich proved his conjecture for the case with genus g = 1. In 1968 Parshin proved a special case (for S = the empty set) of the following theorem: If B is a smooth complex curve and S is a finite subset of B then there exist only finitely many families (up to isomorphism) of smooth curves of fixed genus g ≥ 2 over B \ S. The general case (for non-empty S) of the preceding theorem was proved by Arakelov. At the same time, Parshin gave a new proof (without an application of the Shafarevich finiteness condition) of the Mordell conjecture in function fields (already proved by Yuri Manin in 1963 and by Hans Grauert in 1965). Parshin presented his results in his talk Quelques conjectures de finitude en géométrie diophantienneas an invited speaker at the ICM in 1970 in Nice.
At the ICM in 2010, Parshin was a Plenary Speaker with his talk titled Representations of higher adelic groups and arithmetic.
His other research dealt with generalizations of class field theory in higher dimensions, with integrable systems, and with the history of mathematics.
Parshin was a corresponding member of the Russian Academy of Sciences.
He was an editor for the Russian edition of the collected works of David Hilbert and was a co-editor, with V. I. Arnold, of selected works of Hermann Weyl.
Parshin died on 18 June 2022.
Awards and honors
1996 – Humboldt Prize
2004 – Vinogradov Prize
2012 – Chebyshev Gold Medal
2013 – Honorary doctorate from University of Paris XIII
Selected publications
A. N. Parshin: "Путь. Математика и другие миры" (The Way. Mathematics and Other Worlds) Moscow 2002. (Parshin's writings on Russian science and philosophy)
With Shafarevich, Parshin edited several volumes in the series "Algebraic Geometry and Number Theory" in the Encyclopedia of mathematical sciences published by Springer Verlag.
with Shafarevich: The arithmetic of algebraic varieties. Proc. Steklov Institute Math., 1986, No. 3.
with Yuri Zarin: Finiteness problems in algebraic geometry, in Eight papers translated from the Russian. American Mathematical Society Translations Ser. 2, Vol.143, 1989, pp. 35–102, revised version of the original published as an appendix in the Russian edition of Serge Lang Fundamentals of Diophantine Geometry (English version of the appendix Online)
Parshin Numbers as functions. The development of an idea in the Moscow school of algebraic geometry, in Bolibruch, Osipov, Sinai (eds.) Mathematical Events of the Twentieth Century, Springer 2006, pp. 297–330
Parshin Mathematik in Moskau – es war eine große Epoche, Mitteilungen DMV, Vol. 18, 2010, pp. 43–48
Sources
Sergei Vostokov, Yuri Zarhin (eds.): Algebraic number theory and algebraic geometry: Papers dedicated to A. N. Parshin on his 60th Birthday, American Mathematical Society 2002 (with foreword by Shafarevich)
See also
Parshin chain
Parshin's conjecture
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