Alexei Parshin

Aleksei Nikolaevich ParshinEfn|His name is sometimes romanized as Alexey or Aleksey In 1983, he received his Doctor Nauk (doctorate of sciences) from Moscow State University.

Research

In his 1968 thesis, 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. Shafarevich proved his finiteness conjecture for the case with genus g = 1. Parshin proved a special case (for = the empty set) of the following theorem: If is a smooth complex curve and is a finite subset of then there exist only finitely many families (up to isomorphism) of smooth curves of fixed genus g ≥ 2 over . The general case (for non-empty ) of the preceding theorem was proved by Suren Arakelov in 1971. 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). In 1983, Gerd Faltings completed the program and proved Shafarevich's finiteness conjecture, thereby proving the Mordell conjecture.

Personal life Parshin was born on 7 November 1942 in Sverdlovsk

Parshin was longtime friends with Russian philosopher Aleksei Losev and started the Russian philosophy seminar at the Dom Loseva Library in Moscow. Parshin was Orthodox Christian and wrote about the relationship between Russian religious philosophy and the modern sciences.

Parshin was an invited speaker at the 1970 International Congress of Mathematicians (ICM) with his talk titled Quelques conjectures de finitude en géométrie diophantienne. He was a plenary speaker at the 2010 ICM with his talk titled Representations of higher adelic groups and arithmetic.

Selected publications (Parshin's writings on Russian science and philosophy) with Shafarevich, Parshin edited several volumes in "Algebraic Geometry and Number Theory" in the Encyclopedia of Mathematical Sciences series published by Springer Verlag.

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

Explanatory notes