Persons: Parshin, Alexey Nikolaevich

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Parshin, Alexey Nikolaevich
(1942–2022)

Total publications:	118 (62)
in MathSciNet:	93 (54)
in zbMATH:	74 (43)
in Web of Science:	44 (17)
in Scopus:	28 (23)
Cited articles:	40
Citations:	391
Presentations:	49

Number of views:
This page:	23889
Abstract pages:	50511
Full texts:	19094
References:	2375

Member of the Russian Academy of Sciences

Doctor of physico-mathematical sciences (1983)

Speciality:

01.01.06 (Mathematical logic, algebra, and number theory)

Keywords:

arithmetic surfaces, higher adeles, harmonic analysis, Fourier transform, Poisson summation formulas.

https://www.mathnet.ru/eng/person11177

https://ru.wikipedia.org/wiki/Parshin, Aleksei Nikolaevich

List of publications on Google Scholar

https://zbmath.org/authors/?q=ai:parshin.alexei-n

https://mathscinet.ams.org/mathscinet/MRAuthorID/190005

https://elibrary.ru/author_items.asp?authorid=10742

https://www.webofscience.com/wos/author/record/Q-8379-2016

https://www.scopus.com/authid/detail.url?authorId=7006200324

Full list of publications:

scientific publications

		Citations (Crossref Cited-By Service + Math-Net.Ru)


2020
1.	D. V. Osipov, A. N. Parshin, “Harmonic analysis on the rank-$2$ value group of a two-dimensional local field”, Sb. Math., 211:1 (2020), 115–160

2019
2.	S. O. Gorchinskiy, Vik. S. Kulikov, A. N. Parshin, V. L. Popov, “Igor Rostislavovich Shafarevich and His Mathematical Heritage”, Proc. Steklov Inst. Math., 307 (2019), 1–21
3.	A. N. Parshin, “The Mellin Transform and the Plancherel Theorem for the Discrete Heisenberg Group”, Proc. Steklov Inst. Math., 307 (2019), 174–192

2018
4.	A. N. Parshin, Vestnik RAN, 88:11 (2018), 982–984

2016
5.	D. V. Osipov, A. N. Parshin, “Representations of the Discrete Heisenberg Group on Distribution Spaces of Two-Dimensional Local Fields”, Proc. Steklov Inst. Math., 292 (2016), 185–201

2015
6.	A. N. Parshin, “On the direct image conjecture in the relative Langlands programme”, Russian Math. Surveys, 70:5 (2015), 961–963

2014
7.	A. N. Parshin, “A holomorphic version of the Tate-Iwasawa method for unramified $L$-functions. I”, Sb. Math., 205:10 (2014), 1473–1491

2013
8.	A. N. Parshin, “Generalizations of the Langlands program”, Lecture course, The Langlands program and adelic theory (June 1–8, 2013, SPb), Euler Mathematical Institute, 2013 , http://www.pdmi.ras.ru/EIMI/2013/Lpat/schedule.html
9.	A. N. Parshin, “Base change and automorphic induction in relative dimension 1”, The Langlands program and adelic theory (June 10–14, 2013, SPb), Euler Mathematical Institute, 2013 , http://www.pdmi.ras.ru/EIMI/2013/Lpat/abstracts.pdf
10.	A. N. Parshin, “Teoriya predstavlenii i algebraicheskaya geometriya (novyi vzglyad na starye zadachi)”, I. M. Gelfand i sovremennaya matematika (17–19 dekabrya 2013 g.), MGU, 2013 , http://gelfand100.mech.math.msu.su/cgi-bin/gelfand100.fcgi?lang=ru&page=abstracts

2012
11.	A. N. Parshin, “Questions and remarks to the Langlands programme”, Russian Math. Surveys, 67:3 (2012), 509–539
12.	S. A. Arnal', A. N. Parshin, “On irreducible representations of discrete Heisenberg groups”, Math. Notes, 92:3 (2012), 295–301
13.	A. N. Parshin, “Notes on the Poisson formula”, St. Petersburg Math. J., 23:5 (2012), 781–818

2011
14.	D. V. Osipov, A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. II”, Izv. Math., 75:4 (2011), 749–814
15.	D. V. Osipov, A. N. Parshin, “Harmonic analysis and the Riemann-Roch theorem”, Dokl. Math., 84:3 (2011), 826–829

2010
16.	A. N. Parshin, “Representations of higher adelic groups and arithmetic”, Proceedings of the International Congress of Mathematicians (Hyderabad, India, 19–27 August 2010), Volume 1: Plenary lectures and ceremonies, World Scientific, 2010, 362–392	6 ^[x]
17.	A. N. Parshin, “On holomorphic representations of discrete Heisenberg groups”, Funct. Anal. Appl., 44:2 (2010), 156–159

2008
18.	D. V. Osipov, A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. I”, Izv. Math., 72:5 (2008), 915–976

2006
19.	A. N. Parshin, “Numbers as functions: the development of an idea in the Moscow school of algebraic geometry”, Mathematical events of the twentieth century, Springer, Berlin, 2006, 297–329	3 ^[x]
20.	A. N. Parshin, “Lokalnye konstruktsii v algebraicheskoi geometrii”, Trudy seminara «Globus», 3, 2006, 60–82
21.	S. O. Gorchinskii, A. N. Parshin, “Adelic Lefschetz formula for the action of a one-dimensional torus”, Proceedings of the St. Petersburg Mathematical Society, v. XI, Amer. Math. Soc. Transl. Ser. 2, 218, Amer. Math. Soc., Providence, RI, 2006, 31–48

2003
22.	A. N. Parshin, “Vector Bundles and Arithmetic Groups. II”, Proc. Steklov Inst. Math., 241 (2003), 164–176

2002
23.	A. N. Parshin, “Is it a coincidence?”, Istor.-Mat. Issled. (2), 7(42), 2002, 357–359

2001
24.	A. N. Parshin, “Integrable systems and local fields”, Comm. Algebra, 29:9, Special issue dedicated to Alexei Ivanovich Kostrikin (2001), 4157–4181	20 ^[x]
25.	A. N. Parshin, “The Krichever Correspondence for Algebraic Surfaces”, Funct. Anal. Appl., 35:1 (2001), 74–76
26.	A. N. Parshin, “Note on the Siegel formula”, J. Math. Sci. (New York), 106:5 (2001), 3336–3339

2000
27.	A. N. Parshin, “The Bruhat-Tits buildings over higher dimensional local fields”, Invitation to higher local fields (Münster, August-September 1999), Geom. Topol. Monogr., 3, Geom. Topol. Publ., Coventry, 2000, 223–237 (electronic)	1 ^[x]
28.	A. N. Parshin, “Higher dimensional local fields and $L$-functions”, Invitation to higher local fields (Münster, August-September 1999), Geom. Topol. Monogr., 3, Geom. Topol. Publ., Coventry, 2000, 199–213 (electronic)	11 ^[x]

1999
29.	A. N. Parshin, “On a Ring of Formal Pseudodifferential Operators”, Proc. Steklov Inst. Math., 224 (1999), 266–280

1998
30.	A. N. Parshin, “Kommentarii k rabotam « O variatsionnom ischislenii», (sovm. s M. I. Zelikinym), « Osnovy obschei teorii lineinykh integralnykh uravnenii», glava X «Problema Rimana v teorii funktsii kompleksnogo peremennogo», glava XIX «Teoriya Minkovskogo ob'emov i ploschadei», « Matematicheskie problemy» (sovm. s S. S. Demidovym)”: D. Gilbert, Izbrannye trudy, v. II, Faktorial, M., 1998, 526–529, 535–538, 538–540, 580–591
31.	D. Gilbert, Izbrannye trudy, v. II, eds. A. N. Parshin, Faktorial, M., 1998 , 608 pp.
32.	A. N. Parshin, “Kommentarii k rabotam «O diofantovykh uravneniyakh roda nul», «O diofantovykh uravneniyakh», «O neprivodimosti mnogochlenov s tselochislennymi koeffitsientami»,”: D. Gilbert, Izbrannye trudy, v. I, Faktorial, M., 1998, 518–520, 522–523

1995
33.	A. N. Parshin, On a generalization of the Bruhat-Tits tree, Preprint series: Mathematica Göttingensis, Heft 9, Göttingen Universität, Göttingen, 1995 , 21 pp.
34.	A. N. Parshin, “Vector bundles and arithmetical groups. I”, Proc. Steklov Inst. Math., 208 (1995), 212–233

1994
35.	A. N. Parshin, “Higher Bruhat-Tits buildings and vector bundles on an algebraic surface”, Algebra and number theory (Essen, 1992), de Gruyter, Berlin, 1994, 165–192

1991
36.	A. N. Parshin, “Letter to Don Zagier”, Arithmetic algebraic geometry (Texel, 1989), Progr. Math., 89, Birkhäuser, Boston-Basel-Berlin, MA, 1991, 285–292

1990
37.	A. N. Parshin, “Finiteness theorems and hyperbolic manifolds”, The Grothendieck Festschrift. A collection of articles written in honor of the 60th birthday of Alexander Grothendieck, v. III, Progr. Math., 88, Birkhäuser, Boston–Basel–Berlin, 1990, 163–178

1991
38.	A. N. Parshin, “Galois cohomology and the Brauer group of local fields”, Proc. Steklov Inst. Math., 183 (1991), 191–201

1990
39.	A. N. Parshin, “On the application of ramified coverings in the theory of Diophantine equations”, Math. USSR-Sb., 66:1 (1990), 249–264

1988
40.	A. N. Parshin, “The Bogomolov–Miyaoka–Yau inequality for the arithmetical surfaces and its applications”, Séminaire de Théorie des Nombres, Paris 1986–87, Progr. Math., 75, Birkhäuser, Boston–Basel–Berlin, 1988, 299–312

1986
41.	Yu. G. Zarkhin, A. N. Parshin, “Problemy konechnosti v diofantovoi geometrii”, Prilozhenie k kn.: S. Leng, Osnovy diofantovoi geometrii, Mir, M., 1986, 369–438

1985
42.	A. N. Parshin, “Letter to Pierre Deligne (3 November 1983)”, Société mathématique de France, Astérisque, 127, 1985, 3–5

1986
43.	A. N. Parshin, I. R. Shafarevich, “Arithmetic of algebraic varieties (in the Mathematics Institute of the Academy of Sciences)”, Proc. Steklov Inst. Math., 168 (1986), 75–99

1985
44.	A. N. Parshin, “Local class field theory”, Proc. Steklov Inst. Math., 165 (1985), 157–185

1984
45.	V. I. Arnold, A. N. Parshin, “Kommentarii k rabote: G. Veil. Asimptoticheskii zakon raspredeleniya chastot sobstvennykh kolebanii uprugikh tel proizvolnoi formy”: G. Veil, Izbrannye trudy, Klassiki nauki, Nauka, M., 1984, 446–449

1983
46.	A. N. Parshin, “Chern classes, adeles and $L$-functions”, J. Reine Angew. Math., 341 (1983), 174–192	13 ^[x]
47.	A. N. Parshin, “Adeles and local constants”, Algebraic geometry, Short communications, ICM (Warsaw, 1983), 1983, 12

1978
48.	A. N. Parshin, E. I. Slavutin, “Teoriya invariantov”, Matematika XIX veka, M., Nauka, 1978, 76–81
49.	A. N. Parshin, “Abelian coverings of arithmetic schemes”, Sov. Math. Dokl., 19 (1978), 1438–1442

1977
50.	A. N. Parshin, “Residues and duality on algebraic surfaces”, Uspekhi Mat. Nauk, 32:2(194) (1977), 225–226

1976
51.	A. N. Parshin, “On the arithmetic of two-dimensional schemes. I. Distributions and residues”, Math. USSR-Izv., 10:4 (1976), 695–729

1975
52.	A. N. Parshin, “David Gilbert i teoriya invariantov”, Istoriko-matematicheskie issledovaniya, 20, 1975, 171–197
53.	A. N. Parshin, “Class fields and algebraic $K$-theory”, Uspekhi Mat. Nauk, 30:1(181) (1975), 253–254

1974
54.	A. N. Parshin, “Algebraic curves over functional fields with a finite field of constants”, Math. Notes, 15:4 (1974), 330–335

1973
55.	A. N. Parshin, “Modular correspondences, heights and isogenes of abelian varieties”, Proc. Steklov Inst. Math., 132 (1973), 243–270

1972
56.	A. N. Parshin, “Minimal models of curves of genus 2 and homomorphisms of abelian varieties defined over a field of finite characteristic”, Math. USSR-Izv., 6:1 (1972), 65–108

1971
57.	A. N. Paršin, “Quelques conjectures de finitude en géométrie diophantienne”, Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 1, Gauthier-Villars, Paris, 1971, 467–471

1973
58.	A. N. Parshin, “The arithmetic of algebraic varieties”, J. Soviet Math., 1:5 (1973), 594–620

1970
59.	A. N. Parshin, “Isogenies and torsion of elliptic curves”, Math. USSR-Izv., 4:2 (1970), 415–430

1968
60.	A. N. Parshin, “Algebraic curves over function fields”, Sov. Math. Dokl., 9 (1968), 1419–1422
61.	A. N. Parshin, “Algebraic curves over function fields. I”, Math. USSR-Izv., 2:5 (1968), 1145–1170
62.	I. V. Dolgachev, A. N. Parshin, “The different and discriminant of regular mappings”, Math. Notes, 4:5 (1968), 802–804

1966
63.	A. N. Parshin, “On a certain generalization of Jacobian manifold”, Izv. Akad. Nauk SSSR Ser. Mat., 30:1 (1966), 175–182

Presentations in Math-Net.Ru

1.	Representation theory, complex tori and theta-functions: old and new A. N. Parshin International Conference "Algebraic Geometry: Methods, Relations, and Applications" dedicated to the 80th birthday anniversary of Andrei Nikolaevich Tyurin (1940–2002) February 21, 2020 11:30
2.	Heat equation for theta-functions as a fact of representation theory A. N. Parshin Extended meeting of the seminar "Complex problems of mathematical physics" dedicated to the 70th anniversary of Armen Sergeev March 11, 2019 15:00
3.	Harmonic analysis on discrete groups and analytic properties of zeta-functions of algebraic varieties A. N. Parshin L-Functions and Algebraic Varieties. A conference in memory of Alexey Zykin February 8, 2018 12:30
4.	Zeta-functions in dimension 1 and 2 (continuation) A. N. Parshin Shafarevich Seminar November 14, 2017 15:00
5.	Zeta-functions of schemes in dimension 1 and 2 A. N. Parshin Shafarevich Seminar November 7, 2017 15:00
6.	New results in the theory of $L$-functions A. N. Parshin One-day conference dedicated to the memory of V. A. Iskovskikh December 23, 2014 16:10
7.	Голоморфный вариант метода Тейта–Ивасава и его приложения A. N. Parshin Shafarevich Seminar June 10, 2014 15:00
8.	Теория представлений и алгебраическая геометрия (новый взгляд на старые задачи) A. N. Parshin I. M. Gelfand and Modern Mathematics December 17, 2013 15:00
9.	Letters of foreign scientists A. N. Parshin Общее собрание отделения математических наук РАН, посвященное планам Минобрнауки РФ по реорганизации Российской академии наук July 1, 2013 16:30
10.	Программа Ленглендса и дзета-функции A. N. Parshin International conference dedicated to the 90th anniversary of academician Igor Rostislavovich Shafarevich June 3, 2013 10:30
11.	Base change and automorphic induction for unramified coverings A. N. Parshin Seminar on Arithmetic Algebraic Geometry December 26, 2012 12:00
12.	Complex structures and moduli problem in representation theory A. N. Parshin International conference "KUL!FEST" dedicated to the 60th anniversary of Vik. S. Kulikov December 3, 2012 12:00
13.	Who is Victor Kulikov? A. N. Parshin International conference "KUL!FEST" dedicated to the 60th anniversary of Vik. S. Kulikov December 3, 2012 09:40
14.	Discrete adelic groups A. N. Parshin Seminar on Arithmetic Algebraic Geometry November 7, 2012 12:00
15.	A new kind of functoriality in the Langlands theory A. N. Parshin International Chinese-Russian conference on Number Theory October 12, 2012 14:30
16.	Дзета-функции двумерных схем, соответствие Ленглендса и гипотеза о прямом образе A. N. Parshin Shafarevich Seminar May 29, 2012 15:00
17.	Representation theory of discrete Heisenberg groups A. N. Parshin At Steklov Mathematical Institute of Russian Academy of Sciences January 12, 2012 14:40
18.	Greeting A. N. Parshin One-day conference dedicated to the memory of V. A. Iskovskikh December 29, 2011 11:00
19.	Langlands correspondence and the direct image conjecture A. N. Parshin Seminar on Arithmetic Algebraic Geometry December 14, 2011 12:00
20.	Langlands program (a new sight) A. N. Parshin General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences November 17, 2011 14:00
21.	The problem of modules and classification of irreducible representations A. N. Parshin St. Petersburg Seminar on Representation Theory and Dynamical Systems November 16, 2011 18:00
22.	Classification of schemes and Langlands correspondence A. N. Parshin Seminar on Arithmetic Algebraic Geometry November 2, 2011 12:00
23.	Informal introduction to the Langlands program (continuation) A. N. Parshin Seminar on Arithmetic Algebraic Geometry October 5, 2011 12:00
24.	Informal introduction to the Langlands programm (continuation) A. N. Parshin Seminar on Arithmetic Algebraic Geometry September 28, 2011 12:00
25.	Informal introduction to the Langlands program A. N. Parshin Seminar on Arithmetic Algebraic Geometry September 21, 2011 12:00
26.	Representations theory of adelic groups and arithmetic. Lecture 3 A. Parshin International symposium "Arithmetic days in Moscow" June 16, 2011 10:00
27.	Representations theory of adelic groups and arithmetic. Lecture 2 A. Parshin International symposium "Arithmetic days in Moscow" June 15, 2011 11:20
28.	Representations theory of adelic groups and arithmetic. Lecture 1 A. Parshin International symposium "Arithmetic days in Moscow" June 14, 2011 10:00
29.	Complex structures in the theory of representations of groups A. N. Parshin Seminar "Complex analysis in several variables" (Vitushkin Seminar) April 6, 2011 16:45
30.	Moduli problems in representation theory of groups A. N. Parshin P.K. Rashevskii seminar on tensor and vector analysis with applications in geometry, mechanics and physics March 28, 2011 18:30
31.	Holomorphic duality in representation theory. II A. N. Parshin Seminar on Arithmetic Algebraic Geometry March 2, 2011 13:00
32.	Holomorphic duality in the representation theory of discrete groups A. N. Parshin Seminar on Arithmetic Algebraic Geometry December 29, 2010 11:00
33.	Representation theory of groups and algebraic geometry A. N. Parshin Steklov Mathematical Institute Seminar December 16, 2010 16:00
34.	Introductionary remarks A. N. Parshin Seminar on Arithmetic Algebraic Geometry November 10, 2010 11:00
35.	Теория представлений и алгебраическая геометрия A. N. Parshin Seminar on Arithmetic Algebraic Geometry September 29, 2010 11:00
36.	Representation theory and arithmetic of two-dimensional schemes. III A. N. Parshin Alexey Parshin mini course "Representation theory and arithmetic of two-dimensional schemes" November 20, 2009 15:30
37.	Representation theory and arithmetic of two-dimensional schemes. II A. N. Parshin Alexey Parshin mini course "Representation theory and arithmetic of two-dimensional schemes" November 19, 2009 15:30
38.	Representation theory and arithmetic of two-dimensional schemes. I A. N. Parshin Alexey Parshin mini course "Representation theory and arithmetic of two-dimensional schemes" November 17, 2009 18:00
39.	Неразветвленные $L$-функции и комплексный анализ A. N. Parshin Seminar by Algebra Department October 27, 2009
40.	Representations of discrete nilpotent groups and algebraic geometry A. N. Parshin International conference "Geometry of Algebraic Varieties" dedicated to the memory of Vasily Alexeevich Iskovskikh June 30, 2009 11:15
41.	Open ceremony D. O. Orlov, A. G. Sergeev, A. N. Parshin, M. Reid, V. V. Shokurov International conference "Geometry of Algebraic Varieties" dedicated to the memory of Vasily Alexeevich Iskovskikh June 29, 2009 10:00
42.	Adelic groups (representation theory and related reasults) A. N. Parshin The second annual conference-meeting MIAN–POMI "Algebra and Algebraic Geometry" December 25, 2008 12:00
43.	Speech at the opening of the conference “Algebra and Algebraic Geometry” A. N. Parshin The second annual conference-meeting MIAN–POMI "Algebra and Algebraic Geometry" December 24, 2008 10:35
44.	Анализ на локальных полях и группах аделей (продолжение) A. N. Parshin Seminar by Algebra Department May 16, 2006
45.	Анализ на локальных полях и группах аделей A. N. Parshin Seminar by Algebra Department April 25, 2006
46.	Арифметика и квантовая теория поля A. N. Parshin Seminar on Arithmetic Algebraic Geometry November 30, 2005
47.	Арифметика и квантовая теория поля (анализ и двойственность) A. N. Parshin Seminar by Algebra Department October 25, 2005
48.	Адельная формула Лефшеца S. O. Gorchinskiy, A. N. Parshin Seminar by Algebra Department November 23, 2004
49.	On a generalization of the KP hierarchy A. N. Parshin General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences October 9, 2003

Books in Math-Net.Ru

Algebra, number theory, and algebraic geometry, Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich, Trudy Mat. Inst. Steklova, 307, ed. A. N. Parshin, V. L. Popov, S. O. Gorchinskiy, Vik. S. Kulikov, 2019, 328 с.
http://mi.mathnet.ru/book1773
Number theory, algebra, and analysis, Collected papers. Dedicated to Professor Anatolii Alekseevich Karatsuba on the occasion of his 75th birthday, Trudy Mat. Inst. Steklova, 276, ed. A. N. Parshin, A. G. Sergeev, 2012, 288 с.
http://mi.mathnet.ru/book1375
Number theory, algebra, and algebraic geometry, Collected papers. Dedicated to the 80th birthday of academician Igor' Rostislavovich Shafarevich, Trudy Mat. Inst. Steklova, 241, ed. A. N. Parshin, E. F. Mishchenko, 2003, 272 с.
http://mi.mathnet.ru/book254

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