{{Short description|Russian mathematician (1942–2022)}} {{Use dmy dates|date=June 2022}} {{Infobox scientist | name = Aleksei Parshin | native_name = Алексей Паршин | native_name_lang = ru | image = Alexei Parshin.jpg <!--(filename only, i.e. without "File:" prefix)--> | image_size = | image_upright = | alt = | caption = Parshin in 2005 | birth_date = {{birth date |1942|11|7|df=y}} | birth_place = Sverdlovsk, Russian SFSR, Soviet Union | death_date = {{death date and age |2022|06|18 |1942|11|7|df=y}} | death_place = Moscow, Russian Federation | fields = Mathematics | workplaces = {{ubl|Moscow State University|Steklov Institute of Mathematics}} | alma_mater = Steklov Institute of Mathematics | thesis_title = Algebraic curves over function fields | thesis_url = http://dx.doi.org/10.1070/IM1968v002n05ABEH000723 | thesis_year = 1968 | doctoral_advisor = Igor Shafarevich | doctoral_students = | known_for = {{ubl|Parshin chain|Parshin's conjecture|Parshin's trick}} | awards = {{ubl|Humboldt Prize (1996)|Vinogradov Prize (2004)|Chebyshev Gold Medal (2012)}} | spouse = <!--(or | spouses = )--> | partner = <!--(or | partners = )--> | children = | footnotes = }}
'''Aleksei Nikolaevich Parshin'''{{Efn|His name is sometimes romanized as '''Alexey''' or '''Aleksey'''<ref name="sixtieth-intro"/> and '''Paršin'''.<ref name="thesis"/>}} ({{langx|ru|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.
==Education and career== Parshin entered the Faculty of Mathematics and Mechanics of Moscow State University in 1959 and graduated in 1964.<ref name="seventieth"/><ref name="ae-CV"/> He 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.<ref name="ae-CV">{{cite web |url=https://www.ae-info.org/ae/Member/Parshin_Alexey/CV |title=Alexey Parshin – Curriculum Vitae |website=Academia Europaea |access-date=20 June 2022}}</ref><ref name="thesis">{{cite journal|last=Paršin |first=A. N. |title=Algebraic curves over function fields. |language=Russian |journal=Dokl. Akad. Nauk SSSR |volume=183 |year=1968 |issue=5 |pages=524–526|doi=10.1070/IM1968v002n05ABEH000723 |bibcode=1968IzMat...2.1145P }}</ref> In 1983, he received his ''Doctor Nauk'' (doctorate of sciences) from Moscow State University.<ref name="sixtieth-intro"/><ref name="ae"/>
Parshin became a junior research fellow at the Steklov Institute of Mathematics in Moscow in 1968, later becoming a senior and leading research fellow.<ref name="ae"/><ref name="seventieth"/> He became the head of its Department of Algebra in 1995.<ref name="ae"/><ref name="seventieth"/> He also taught at Moscow State University.<ref name="seventieth">{{cite journal |first1=Sergei V. |last1=Vostokov |first2=Sergey O. |last2=Gorchinskiy |first3=Alexander B. |last3=Zheglov |first4=Yurii G. |last4=Zarkhin |first5=Yuri V. |last5=Nesterenko |first6=Dmitri O. |last6=Orlov |first7=Denis V. |last7=Osipov |first8=Vladimir L. |last8=Popov |first9=Armen G. |last9=Sergeev |first10=Igor R. |last10=Shafarevich |title=Aleksei Nikolaevich Parshin (on his 70th birthday) |journal=Russian Mathematical Surveys |volume=68 |issue=1 |pages=189–197 |year=2013 |doi=10.1070/RM2013v068n01ABEH004827|bibcode=2013RuMaS..68..189V |s2cid=123001679 }}</ref>
==Research== {{see also|Parshin chain|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.<ref>{{cite journal|title=Algebraic curves over function fields I|last=Parshin|first=A. N.|authorlink=Aleksei Parshin|journal=Izv. Akad. Nauk SSSR Ser. Mat.|volume=32|year=1968|issue=5|pages=1191–1219|doi=10.1070/IM1968v002n05ABEH000723|bibcode=1968IzMat...2.1145P}}</ref><ref name="Cornell-Silverman">{{cite book|title=Arithmetic geometry. Papers from the conference held at the University of Connecticut, Storrs, Connecticut, July 30 – August 10, 1984 |editor1-last=Cornell | editor1-first=Gary | editor2-link=Joseph Hillel Silverman| editor2-last=Silverman | editor2-first=Joseph H. |year=1986 |publisher=Springer-Verlag |location= New York |isbn=0-387-96311-1 | doi=10.1007/978-1-4613-8655-1 | mr=861969}}</ref> Shafarevich proved his finiteness conjecture for the case with genus ''g'' = 1. Parshin proved a special case (for {{math|''S''}} = the empty set) of the following theorem: If {{math|''B''}} is a smooth complex curve and {{math|''S''}} is a finite subset of {{math|''B''}} then there exist only finitely many families (up to isomorphism) of smooth curves of fixed genus ''g'' ≥ 2 over {{math|''B'' \ ''S''}}.<ref name=CaporasoRef>{{cite arXiv|eprint=math/0004078|title=Remarks about uniform boundedness of rational points over function fields|last=Caporaso|first=Lucia|authorlink=Lucia Caporaso |year=2000 }}</ref> The general case (for non-empty {{math|''S''}}) of the preceding theorem was proved by Suren Arakelov in 1971.<ref name=CaporasoRef/><ref>{{cite arXiv|eprint=math/0311085 |author=Heier, Gordon|title=Uniformly effective Shafarevich conjecture on families of hyperbolic curves over a curve with prescribed degeneracy condition |year=2003}}</ref> 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).<ref>Parshin, [http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=2513&option_lang=eng Algebraic curves over function fields. I], Math. USSR Izvestiya Vol. 2, 1968</ref> In 1983, Gerd Faltings completed the program and proved Shafarevich's finiteness conjecture, thereby proving the Mordell conjecture.<ref name="Cornell-Silverman"/>
His other research dealt with generalizations of class field theory in higher dimensions, with integrable systems, and with the history of mathematics.<ref name="sixtieth-intro">{{cite book |title=Algebraic Number Theory and Algebraic Geometry: Papers Dedicated to A. N. Parshin on the Occasion of his Sixtieth Birthday |editor1-first=Esther V. |editor1-last=Forbes |editor2-first=S. V. |editor2-last=Vostokov |editor2-link=Sergei Vostokov |editor3-first=Yuri |editor3-last=Zarhin |publisher=American Mathematical Society |year=2002 |volume=300 |series=Contemporary Mathematics |isbn=0821832670 |doi=10.1090/conm/300 |page=vii–viii}}</ref><ref name="seventieth"/>
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.<ref name="sixtieth-intro"/><ref>{{cite book |editor1-first=Vladimir |editor1-last=Arnold |editor1-link=Vladimir Arnold |editor2-first=Aleksei |editor2-last=Parshin |title=Hermann Weyl, Selected Papers, Mathematics, Theoretical Physics |publisher=Nauka |location=Moscow |year=1984}}</ref>
==Personal life== Parshin was born on 7 November 1942 in Sverdlovsk<ref name="sixtieth-intro"/><ref name="seventieth"/> and died on 18 June 2022.<ref name="ae"/><ref name="steklov">{{cite web |url=http://www.mi-ras.ru/index.php |title=Mathematical Institute V.A. Steklov Russian Academy of Sciences |website=Steklov Institute of Mathematics |access-date=18 June 2022 |language=ru |archive-url=https://web.archive.org/web/20220620110131/http://www.mi-ras.ru/index.php |archive-date=20 June 2022 |url-status=live}}</ref><ref name="steklov-obit">{{cite web |url=http://www.mi-ras.ru/news/22/Parshin_obituary.pdf |title=Алексей Николаевич ПАРШИН |trans-title=Aleksei Nikolaevich Parshin |website=Steklov Institute of Mathematics |access-date=21 June 2022 |language=ru}}</ref>
Parshin was longtime friends with Russian philosopher Aleksei Losev and started the Russian philosophy seminar at the Dom Loseva Library in Moscow.<ref name="domloseva">{{cite web |url=http://domloseva.ru/events/news/filosofiya/aleksej-nikolaevich-parshin-akademik-ran-vechnaya-pamyat |website=Dom Loseva Library |title=Алексей Николаевич Паршин, академик РАН. Вечная память! |trans-title=Alexei Nikolaevich Parshin, Academician of the Russian Academy of Sciences. Everlasting memory! |date=21 June 2022 |access-date=22 June 2022 |language=ru}}</ref> Parshin was Orthodox Christian and wrote about the relationship between Russian religious philosophy and the modern sciences.<ref name="domloseva"/>
==Awards and honors== In 1971, Parshin received the Prize of the Moscow Mathematical Society for young mathematicians.<ref name="ae"/> He was awarded the Humboldt Prize in 1996.<ref name="seventieth"/><ref name="ae"/> He received the Vinogradov Prize in 2004 and the Chebyshev Gold Medal in 2012 from the Russian Academy of Sciences.<ref name="seventieth"/><ref name="ae"/>
The Université Paris-Nord granted Parshin an honorary doctorate in 2001.<ref name="ae"/><ref name="sixtieth-intro"/> Parshin was elected a corresponding member of the Russian Academy of Sciences in 2006 and then a full member in 2011.<ref name="ae"/> He was elected a member of the Academia Europaea in 2017.<ref name="ae">{{cite web |url=https://www.ae-info.org/ae/Member/Parshin_Alexey |title=Parshin Alexey |website=Academia Europaea |access-date=20 June 2022}}</ref>
Parshin was an invited speaker at the 1970 International Congress of Mathematicians (ICM) with his talk titled ''Quelques conjectures de finitude en géométrie diophantienne''.<ref name="ae"/><ref>Paršin, A. N. [http://www.mathunion.org/ICM/ICM1970.1/Main/icm1970.1.0467.0472.ocr.pdf "Quelques conjectures de finitude en géométrie Diophantienne."] {{Webarchive|url=https://web.archive.org/web/20160924235505/http://www.mathunion.org/ICM/ICM1970.1/Main/icm1970.1.0467.0472.ocr.pdf |date=24 September 2016 }} In Actes, Congrès intern. math, Tome 1, vol. 1, pp. 467–471. 1970.</ref> He was a plenary speaker at the 2010 ICM with his talk titled ''Representations of higher adelic groups and arithmetic''.<ref name="ae"/><ref>Parshin, A. N. [https://books.google.com/books?hl=en&lr=&id=GFE1vx2pynMC&pg=PA362 "Representations of higher adelic groups and arithmetic."] In Proceedings of the International Congress of Mathematicians, vol. 1, pp. 362–392. 2011.</ref>
==Selected publications== * {{cite book |first1=A. N. |last1= Parshin |title=Путь. Математика и другие миры |trans-title=The Way. Mathematics and Other Worlds |publisher=Добросвет |location=Moscow |date=2002 |isbn=978-5-7913-0053-9 |url=https://books.google.com/books?id=zb4eAQAAIAAJ |language=ru}} (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. ** {{cite book |editor1-last=Parshin |editor1-first=A. N. |editor2-last=Shafarevich |editor2-first=I. R. |title=Algebraic Geometry III – Complex Algebraic Varieties Algebraic Curves and Their Jacobians |series=Encyclopaedia of Mathematical Sciences |date=1998 |volume=36 |doi=10.1007/978-3-662-03662-4 |isbn=978-3-642-08118-7 |url=https://link.springer.com/book/10.1007/978-3-662-03662-4 |access-date=24 June 2022 }} ** {{cite book |editor1-last=Parshin |editor1-first=A. N. |editor2-last=Shafarevich |editor2-first=I. R. |title=Algebraic Geometry IV – Linear Algebraic Groups Invariant Theory |series=Encyclopaedia of Mathematical Sciences |date=1994 |volume=55 |doi=10.1007/978-3-662-03073-8 |isbn=978-3-642-08119-4 |url=https://link.springer.com/book/10.1007/978-3-662-03073-8 |access-date=24 June 2022 |language=en}} ** {{cite book |editor1-last=Parshin |editor1-first=A. N. |editor2-last=Shafarevich |editor2-first=I. R. |title=Algebraic Geometry V – Fano Varieties |date=1999 |volume=47 |publisher=Springer |isbn=978-3-642-08260-3 |url=https://link.springer.com/book/9783540614685 |access-date=24 June 2022}} ** {{cite book |editor1-last=Parshin |editor1-first=A.vN. |editor2-last=Shafarevich |editor2-first=I. R. |title=Number Theory IV – Transcendental Numbers |series=Encyclopaedia of Mathematical Sciences |date=1998 |volume=44 |doi=10.1007/978-3-662-03644-0 |url=https://link.springer.com/book/10.1007/978-3-662-03644-0 |language=en |isbn=978-3-662-03644-0 |access-date=24 June 2022}} * {{cite journal |last1=Parshin |first1=A. N. |last2=Shafarevich |first2=I. R. |title=Arithmetic of algebraic varieties |journal=Proceedings of the Steklov Institute of Mathematics |date=1986 |volume=168 |issue=3 |pages=75–99 |url=http://mi.mathnet.ru/eng/tm/v168/p72}} * 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 [http://www.arxiv.org/abs/0912.4325 Online]) * Parshin [https://arxiv.org/abs/0912.3785 ''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 [http://page.math.tu-berlin.de/~mdmv/archive/18/mdmv-18-1-043.pdf ''Mathematik in Moskau – es war eine große Epoche''], Mitteilungen DMV, Vol. 18, 2010, pp. 43–48
== Explanatory notes == {{Notelist}}
==References== {{Reflist}}
==External links== * [http://www.mathnet.ru/php/person.phtml?option_lang=eng&personid=11177 Parshin at mathnet.ru] * {{DNB-Portal|172519012}} * {{MathGenealogy|249334}}
{{Authority control}}
{{DEFAULTSORT:Parshin, Aleksei Nikolaevich}} Category:1942 births Category:2022 deaths Category:20th-century Russian mathematicians Category:21st-century Russian mathematicians Category:Arithmetic geometers Category:Corresponding Members of the Russian Academy of Sciences Category:Eastern Orthodox Christians from Russia Category:Full Members of the Russian Academy of Sciences Category:Humboldt Research Award recipients Category:Moscow State University alumni Category:Academic staff of Moscow State University Category:Scientists from Yekaterinburg Category:Soviet mathematicians