Aleksei Parshin

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Aleksei Parshin
Алексей Паршин
Humboldt Prize (1996)
  • Vinogradov Prize (2004)
  • Chebyshev Gold Medal (2012)
    • Scientific career
    FieldsMathematics
    Institutions
    ThesisAlgebraic curves over function fields (1968)
    Doctoral advisorIgor Shafarevich

    Aleksei Nikolaevich Parshin

    Mordell conjecture
    .

    Education and career

    Parshin entered the Faculty of Mathematics and Mechanics of

    Doctor Nauk (doctorate of sciences) from Moscow State University.[1][5]

    Parshin became a junior research fellow at the Steklov Institute of Mathematics in Moscow in 1968, later becoming a senior and leading research fellow.[5][3] He became the head of its Department of Algebra in 1995.[5][3] He also taught at Moscow State University.[3]

    Research

    See also: Parshin chain and Parshin's conjecture

    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.[6][7] Shafarevich proved his finiteness conjecture for the case with genus g = 1. 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.[8] The general case (for non-empty S) of the preceding theorem was proved by Suren Arakelov in 1971.[8][9] 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).[10] In 1983, Gerd Faltings completed the program and proved Shafarevich's finiteness conjecture, thereby proving the Mordell conjecture.[7]

    His other research dealt with generalizations of class field theory in higher dimensions, with integrable systems, and with the history of mathematics.[1][3]

    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.[1][11]

    Personal life

    Parshin was born on 7 November 1942 in Sverdlovsk[1][3] and died on 18 June 2022.[5][12][13]

    Parshin was longtime friends with Russian philosopher Aleksei Losev and started the Russian philosophy seminar at the Dom Loseva Library in Moscow.[14] Parshin was Orthodox Christian and wrote about the relationship between Russian religious philosophy and the modern sciences.[14]

    Awards and honors

    In 1971, Parshin received the Prize of the

    Humboldt Prize in 1996.[3][5] He received the Vinogradov Prize in 2004 and the Chebyshev Gold Medal in 2012 from the Russian Academy of Sciences.[3][5]

    The

    Université Paris-Nord granted Parshin an honorary doctorate in 2001.[5][1] Parshin was elected a corresponding member of the Russian Academy of Sciences in 2006 and then a full member in 2011.[5] He was elected a member of the Academia Europaea in 2017.[5]

    Parshin was an invited speaker at the 1970 International Congress of Mathematicians (ICM) with his talk titled Quelques conjectures de finitude en géométrie diophantienne.[5][15] He was a plenary speaker at the 2010 ICM with his talk titled Representations of higher adelic groups and arithmetic.[5][16]

    Selected publications

    Explanatory notes

    1. ^ His name is sometimes romanized as Alexey or Aleksey[1] and Paršin.[2]

    References

    1. ^
      ISBN 0821832670
      .
    2. ^
      doi:10.1070/IM1968v002n05ABEH000723
      .
    3. ^
      S2CID 123001679
      .
    4. ^ a b "Alexey Parshin – Curriculum Vitae". Academia Europaea. Retrieved 20 June 2022.
    5. ^ a b c d e f g h i j k l "Parshin Alexey". Academia Europaea. Retrieved 20 June 2022.
    6. doi:10.1070/IM1968v002n05ABEH000723
      .
    7. ^
      MR 0861969
      .
    8. ^
      arXiv:math/0004078
      .
    9. arXiv:math/0311085
      .
    10. ^ Parshin, Algebraic curves over function fields. I, Math. USSR Izvestiya Vol. 2, 1968
    11. ^ Arnold, Vladimir; Parshin, Aleksei, eds. (1984). Hermann Weyl, Selected Papers, Mathematics, Theoretical Physics. Moscow: Nauka.
    12. ^ "Mathematical Institute V.A. Steklov Russian Academy of Sciences". Steklov Institute of Mathematics (in Russian). Archived from the original on 20 June 2022. Retrieved 18 June 2022.
    13. ^ "Алексей Николаевич ПАРШИН" [Aleksei Nikolaevich Parshin] (PDF). Steklov Institute of Mathematics (in Russian). Retrieved 21 June 2022.
    14. ^ a b "Алексей Николаевич Паршин, академик РАН. Вечная память!" [Alexei Nikolaevich Parshin, Academician of the Russian Academy of Sciences. Everlasting memory!]. Dom Loseva Library (in Russian). 21 June 2022. Retrieved 22 June 2022.
    15. ^ Paršin, A. N. "Quelques conjectures de finitude en géométrie Diophantienne." Archived 24 September 2016 at the Wayback Machine In Actes, Congrès intern. math, Tome 1, vol. 1, pp. 467–471. 1970.
    16. ^ Parshin, A. N. "Representations of higher adelic groups and arithmetic." In Proceedings of the International Congress of Mathematicians, vol. 1, pp. 362–392. 2011.

    External links

    Retrieved from "https://en.wikipedia.org/w/index.php?title=Aleksei_Parshin&oldid=1172893801"