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Parshin Aleksei Nikolaevich
(full list of publications)
| by years | scientific publications | by types |



   2016
1. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus

   2015
2. A. N. Parshin, “On the direct image conjecture in the relative Langlands programme”, Russian Math. Surveys, 70:5 (2015), 961–963  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus

   2014
3. A. N. Parshin, “A holomorphic version of the Tate-Iwasawa method for unramified $L$-functions. I”, Sb. Math., 205:10 (2014), 1473–1491  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus

   2013
4. 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
5. 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
6. 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
7. A. N. Parshin, “Questions and remarks to the Langlands programme”, Russian Math. Surveys, 67:3 (2012), 509–539  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 2)
8. S. A. Arnal', A. N. Parshin, “On irreducible representations of discrete Heisenberg groups”, Math. Notes, 92:3 (2012), 295–301  mathnet  crossref  crossref  zmath  isi (cited: 3)  elib (cited: 5)  elib (cited: 5)  scopus (cited: 3)

   2011
9. A. N. Parshin, “Zapiski o formule Puassona”, Algebra i analiz, 23:5 (2011), 1–54  mathnet (cited: 3)  mathscinet (cited: 1)  elib (cited: 4); A. N. Parshin, “Notes on the Poisson formula”, St. Petersburg Math. J., 23:5 (2012), 781–818  crossref  mathscinet  isi (cited: 2)  elib (cited: 3)  scopus (cited: 2)
10. D. V. Osipov, A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. II”, Izv. Math., 75:4 (2011), 749–814  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 8)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 2)
11. D. V. Osipov, A. N. Parshin, “Harmonic analysis and the Riemann-Roch theorem”, Dokl. Math., 84:3 (2011), 826–829  crossref  mathscinet  isi (cited: 2)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 2)

   2010
12. 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  crossref  mathscinet (cited: 7)
13. A. N. Parshin, “On holomorphic representations of discrete Heisenberg groups”, Funct. Anal. Appl., 44:2 (2010), 156–159  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 8)  elib (cited: 9)  elib (cited: 9)  scopus (cited: 7)

   2008
14. D. V. Osipov, A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. I”, Izv. Math., 72:5 (2008), 915–976  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 8)  elib  scopus (cited: 4)

   2006
15. 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  crossref  mathscinet (cited: 3)  zmath
16. A. N. Parshin, “Lokalnye konstruktsii v algebraicheskoi geometrii”, Trudy seminara «Globus», 3, 2006, 60–82  mathscinet

   2005
17. S. O. Gorchinskii, A. N. Parshin, “Adelnaya formula Lefshetsa dlya deistviya odnomernogo tora”, Trudy Sankt-Peterburgskogo matematicheskogo obschestva, 11, 2005, 37–57  mathscinet  zmath; 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  mathscinet  zmath

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

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

   2001
20. A. N. Parshin, “Integrable systems and local fields”, Comm. Algebra, 29:9, Special issue dedicated to Alexei Ivanovich Kostrikin (2001), 4157–4181  crossref  mathscinet (cited: 10)  zmath  isi (cited: 13)  elib (cited: 13)  scopus (cited: 12)
21. A. N. Parshin, “The Krichever Correspondence for Algebraic Surfaces”, Funct. Anal. Appl., 35:1 (2001), 74–76  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 6)  elib (cited: 5)  scopus (cited: 5)
22. A. N. Parshin, “Note on the Siegel formula”, J. Math. Sci. (New York), 106:5 (2001), 3336–3339  mathnet  crossref  mathscinet  zmath  elib (cited: 1)

   2000
23. 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)  crossref  mathscinet (cited: 1)  zmath
24. 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)  crossref  mathscinet (cited: 9)  zmath

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

   1998
26. 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
27. D. Gilbert, Izbrannye trudy, v. II, eds. A. N. Parshin, Faktorial, M., 1998 , 608 pp.
28. 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
29. A. N. Parshin, On a generalization of the Bruhat-Tits tree, Preprint series: Mathematica Göttingensis, Heft 9, Göttingen Universität, Göttingen, 1995 , 21 pp.
30. A. N. Parshin, “Vector bundles and arithmetical groups. I”, Proc. Steklov Inst. Math., 208 (1995), 212–233  mathnet  mathscinet  zmath

   1994
31. 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  mathscinet (cited: 2)  zmath

   1991
32. A. N. Parshin, “Letter to Don Zagier”, Arithmetic algebraic geometry (Texel, 1989), Progr. Math., 89, Birkhäuser, Boston-Basel-Berlin, MA, 1991, 285–292  mathscinet (cited: 2)

   1990
33. 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  mathscinet (cited: 2)  zmath
34. A. N. Parshin, “Kogomologii Galua i gruppa Brauera lokalnykh polei”, Teoriya Galua, koltsa, algebraicheskie gruppy i ikh prilozheniya, Sbornik statei, Tr. MIAN SSSR, 183, Nauka. Leningradskoe otd., L., 1990, 159–169  mathnet (cited: 5)  mathscinet (cited: 12)  zmath; A. N. Parshin, “Galois cohomology and the Brauer group of local fields”, Proc. Steklov Inst. Math., 183 (1991), 191–201  mathscinet  zmath

   1989
35. A. N. Parshin, “O primenenii razvetvlennykh nakrytii v teorii diofantovykh uravnenii”, Matem. sb., 180:2 (1989), 244–259  mathnet (cited: 1)  mathscinet (cited: 3)  zmath; A. N. Parshin, “On the application of ramified coverings in the theory of Diophantine equations”, Math. USSR-Sb., 66:1 (1990), 249–264  crossref  mathscinet  zmath  isi (cited: 1)

   1988
36. 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  mathscinet (cited: 9)

   1986
37. Yu. G. Zarkhin, A. N. Parshin, “Problemy konechnosti v diofantovoi geometrii”, Prilozhenie k kn.: S. Leng, Osnovy diofantovoi geometrii, Mir, M., 1986, 369–438  mathscinet (cited: 2)

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

   1984
39. A. N. Parshin, I. R. Shafarevich, “Arifmetika algebraicheskikh mnogoobrazii (v otdele algebry MIAN)”, Algebra, matematicheskaya logika, teoriya chisel, topologiya, Sbornik obzornykh statei. 1. K 50-letiyu Instituta, Tr. MIAN SSSR, 168, 1984, 72–97  mathnet (cited: 1)  mathscinet  zmath; 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  mathscinet  zmath
40. A. N. Parshin, “Lokalnaya teoriya polei klassov”, Algebraicheskaya geometriya i ee prilozheniya, Sbornik statei, Tr. MIAN SSSR, 165, 1984, 143–170  mathnet (cited: 17)  mathscinet (cited: 32)  zmath; A. N. Parshin, “Local class field theory”, Proc. Steklov Inst. Math., 165 (1985), 157–185  mathscinet  zmath
41. 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
42. A. N. Parshin, “Chern classes, adeles and $L$-functions”, J. Reine Angew. Math., 341 (1983), 174–192  crossref  mathscinet (cited: 22)  zmath  isi (cited: 35)
43. A. N. Parshin, “Adeles and local constants”, Algebraic geometry, Short communications, ICM (Warsaw, 1983), 1983, 12

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

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

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

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

   1974
50. A. N. Parshin, “Algebraic curves over functional fields with a finite field of constants”, Math. Notes, 15:4 (1974), 330–335  mathnet  crossref  mathscinet  zmath  elib  scopus

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

   1972
52. 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  mathnet  crossref  mathscinet  zmath

   1971
53. 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  mathscinet (cited: 2)  zmath
54. A. N. Parshin, “Arifmetika algebraicheskikh mnogoobrazii”, Itogi nauki. Ser. Mat. Algebra. Topol. Geom. 1970, VINITI, M., 1971, 111–151  mathnet (cited: 1)  mathscinet  zmath; A. N. Parshin, “The arithmetic of algebraic varieties”, J. Soviet Math., 1:5 (1973), 594–620  crossref  mathscinet  zmath  scopus (cited: 2)

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

   1968
56. A. N. Parshin, “Algebraic curves over function fields”, Sov. Math. Dokl., 9 (1968), 1419–1422  mathscinet  zmath
57. A. N. Parshin, “Algebraic curves over function fields. I”, Math. USSR-Izv., 2:5 (1968), 1145–1170  mathnet  crossref  mathscinet  zmath
58. I. V. Dolgachev, A. N. Parshin, “The different and discriminant of regular mappings”, Math. Notes, 4:5 (1968), 802–804  mathnet  crossref  mathscinet  zmath  scopus (cited: 1)

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