Aleksei Nikolaevich Parshin (; 7 November 1942 – 18 June 2022) was a Russian mathematician, specializing in

arithmetic geometry In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties. ...

. He is most well-known for his role in the proof of the Mordell conjecture.

Education and career

Parshin entered the Faculty of Mathematics and Mechanics of

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

in 1959 and graduated in 1964. He then enrolled as a graduate student at the

Steklov Institute of Mathematics Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Stek ...

, where he received his '' Kand. Nauk'' (Ph.D.) in 1968 under

Igor Shafarevich Igor Rostislavovich Shafarevich (; 3 June 1923 – 19 February 2017) was a Soviet and Russian mathematician who contributed to algebraic number theory and algebraic geometry. Outside mathematics, he wrote books and articles that criticised social ...

. In 1983, he received his ''

Doctor Nauk A Doctor of Sciences, abbreviated д-р наук or д. н.; ; ; ; is a higher doctoral degree in the Russian Empire, Soviet Union and many Commonwealth of Independent States countries. One of the prerequisites of receiving a Doctor of Sciences ...

'' (doctorate of sciences) from Moscow State University. Parshin became a junior research fellow at the Steklov Institute of Mathematics in Moscow in 1968, later becoming a senior and leading research fellow. He became the head of its Department of Algebra in 1995. He also taught at 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 In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a smooth projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular f ...

via what is known as ''Parshin's trick'', which gives an embedding of an

algebraic curve In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane cu ...

into the

Siegel modular variety In mathematics, a Siegel modular variety or Siegel moduli space is an algebraic variety that parametrizes certain types of abelian varieties of a fixed dimension. More precisely, Siegel modular varieties are the moduli spaces of principally pola ...

. 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 Suren Yurievich Arakelov (, ) (born October 16, 1947 in Kharkiv) is a Soviet mathematician of Armenian descent known for developing Arakelov theory. Biography From 1965 onwards Arakelov attended the Mathematics department of Moscow State Univers ...

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 Yuri Ivanovich Manin (; 16 February 1937 – 7 January 2023) was a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics. Life an ...

in 1963 and by

Hans Grauert Hans Grauert (8 February 1930 in Haren, Emsland, Germany – 4 September 2011) was a German mathematician. He is known for major works on several complex variables, complex manifolds and the application of sheaf theory in this area, which i ...

in 1965). In 1983,

Gerd Faltings Gerd Faltings (; born 28 July 1954) is a German mathematician known for his work in arithmetic geometry. Education From 1972 to 1978, Faltings studied mathematics and physics at the University of Münster. Interrupted by 15 months of obligatory ...

completed the program and proved Shafarevich's finiteness conjecture, thereby proving the Mordell conjecture. His other research dealt with generalizations of

class field theory In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. Hilbert is credit ...

in higher dimensions, with integrable systems, and with the history of mathematics. He was an editor for the Russian edition of the collected works of

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...

and was a co-editor, with V. I. Arnold, of selected works of

Hermann Weyl Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, ...

Personal life

Parshin was born on 7 November 1942 in Sverdlovsk and died on 18 June 2022. Parshin was longtime friends with Russian philosopher

Aleksei Losev Aleksei Fyodorovich Losev (; 22 September 1893 – 24 May 1988) was a Soviet and Russian Philosophy, philosopher, Philology, philologist and culturology, culturologist, one of the most prominent figures in Russian philosophy, Russian philosophica ...

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.

Awards and honors

In 1971, Parshin received the Prize of the

Moscow Mathematical Society The Moscow Mathematical Society (MMS) is a society of Moscow mathematicians aimed at the development of mathematics in Russia. It was created in 1864, and Victor Vassiliev is the current president. History The first meeting of the society w ...

for young mathematicians. He was awarded the

Humboldt Prize The Humboldt Research Award (), also known informally as the Humboldt Prize, is an award given by the Alexander von Humboldt Foundation of Germany to internationally renowned scientists and scholars who work outside of Germany in recognition of ...

in 1996. He received the Vinogradov Prize in 2004 and the

Chebyshev Gold Medal Pafnuty Lvovich Chebyshev ( rus, Пафну́тий Льво́вич Чебышёв, p=pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof) ( – ) was a Russian mathematician and considered to be the founding father of Russian mathematics. Chebysh ...

in 2012 from the Russian Academy of Sciences. The

Université Paris-Nord Sorbonne Paris North University () is a public university based in Paris, France. It is one of the thirteen universities that succeeded the University of Paris in 1968. It is a multidisciplinary university located in north of Paris, in the munici ...

granted Parshin an honorary doctorate in 2001. Parshin was elected a corresponding member of the

Russian Academy of Sciences The Russian Academy of Sciences (RAS; ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such ...

in 2006 and then a full member in 2011. He was elected a member of the

Academia Europaea The Academia Europaea is a pan-European Academy of humanities, letters, law, and sciences. The Academia was founded in 1988 as a functioning Europe-wide Academy that encompasses all fields of scholarly inquiry. It acts as co-ordinator of Europe ...

in 2017. Parshin was an invited speaker at the 1970

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

(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''.Parshin, A. N
"Representations of higher adelic groups and arithmetic."
In Proceedings of the International Congress of Mathematicians, vol. 1, pp. 362–392. 2011.

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 Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

. ** ** ** ** * * 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 Serge Lang (; May 19, 1927 – September 12, 2005) was a French-American mathematician and activist who taught at Yale University for most of his career. He is known for his work in number theory and for his mathematics textbooks, including the i ...

''Fundamentals of Diophantine Geometry'' (English version of the appendi
Online
* Parshi
''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 * Parshi
''Mathematik in Moskau – es war eine große Epoche''
Mitteilungen DMV, Vol. 18, 2010, pp. 43–48

Explanatory notes

References

External links

Parshin at mathnet.ru
* * {{DEFAULTSORT:Parshin, Aleksei Nikolaevich 1942 births 2022 deaths 20th-century Russian mathematicians 21st-century Russian mathematicians Arithmetic geometers Corresponding Members of the Russian Academy of Sciences Eastern Orthodox Christians from Russia Full Members of the Russian Academy of Sciences Humboldt Research Award recipients Moscow State University alumni Academic staff of Moscow State University Scientists from Yekaterinburg Soviet mathematicians