A. N. Parshin, “On the arithmetic of two-dimensional schemes. I. Distributions and residues”, Izv. Akad. Nauk SSSR Ser. Mat., 40:4 (1976), 736–773; Math. USSR-Izv., 10:4 (1976), 695

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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 4, Pages 736–773 (Mi izv2201)

This article is cited in 43 scientific papers (total in 44 papers)

On the arithmetic of two-dimensional schemes. I. Distributions and residues

A. N. Parshin

Abstract: This paper is devoted to the generalization of the theory of distributions (adeles) on schemes of dimension 2.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:4, 695–729

Bibliographic databases:

UDC: 513.6
MSC: Primary 14G99, 14F05; Secondary 14F99
Received: 13.01.1976

Citation: A. N. Parshin, “On the arithmetic of two-dimensional schemes. I. Distributions and residues”, Izv. Akad. Nauk SSSR Ser. Mat., 40:4 (1976), 736–773; Math. USSR-Izv., 10:4 (1976), 695–729

Citation in format AMSBIB

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\crossref{https://doi.org/10.1070/IM1976v010n04ABEH001810}

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:

V. G. Lomadze, “On the ramification theory of two-dimensional local fields”, Math. USSR-Sb., 37:3 (1980), 349–365
A. A. Beilinson, “Residues and adeles”, Funct. Anal. Appl., 14:1 (1980), 34–35
V. G. Lomadze, “On residues in algebraic geometry”, Math. USSR-Izv., 19:3 (1982), 495–520
S. V. Vostokov, “Explicit construction of class field theory for a multidimensional local field”, Math. USSR-Izv., 26:2 (1986), 263–287
Zhongming Tang, “An algebraic approach to the residues in algebraic geometry”, Math Z, 203:1 (1990), 1
A. Huber, “On the Parshin-Beilinson Adeles for schemes”, Abh Math Sem Hamburg, 61:1 (1991), 249
Reinhold Hübl, “Residues of regular and meromorphic differential forms”, Math Ann, 300:1 (1994), 605
Fesenko I., “Abelian Local P-Class Field-Theory”, Math. Ann., 301:3 (1995), 561–586
J. -L. Brylinski, D. A. Mclaughlin, “The geometry of two-dimensional symbols”, K-Theory, 10:3 (1996), 215
Robert A. Bell, “On properties of the n-dimensional norm residue symbol in higher local class field theory”, Journal of Pure and Applied Algebra, 108:1 (1996), 1
Kazuya MATSUMI, “Arithmetic of three-dimensional complete regular local rings of positive characteristics”, Tohoku Math Publ, 13:13 (1999), 1
A. B. Zheglov, “On the classification of two-dimensional local skew fields”, Russian Math. Surveys, 54:4 (1999), 858–859
I-Chiau Huang, “An Explicit Construction of Residual Complexes”, Journal of Algebra, 225:2 (2000), 698
A. N. Parshin, “The Krichever Correspondence for Algebraic Surfaces”, Funct. Anal. Appl., 35:1 (2001), 74–76
A. B. Zheglov, “On the structure of two-dimensional local skew fields”, Izv. Math., 65:1 (2001), 23–55
D. V. Osipov, “Krichever correspondence for algebraic varieties”, Izv. Math., 65:5 (2001), 941–975
Parshin A.N., “Integrable systems and local fields”, Communications in Algebra, 29:9 (2001), 4157–4181
Proc. Steklov Inst. Math., 241 (2003), 98–109
D. V. Osipov, “Central extensions and reciprocity laws on algebraic surfaces”, Sb. Math., 196:10 (2005), 1503–1527
A. B. Zheglov, D. V. Osipov, “On Some Questions Related to the Krichever Correspondence”, Math. Notes, 81:4 (2007), 467–476
S. O. Gorchinskiy, “Adele resolvent for bundles of $K$-groups”, Russian Math. Surveys, 62:1 (2007), 184–186
D. V. Osipov, A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. I”, Izv. Math., 72:5 (2008), 915–976
S. O. Gorchinskiy, “An adelic resolution for homology sheaves”, Izv. Math., 72:6 (2008), 1187–1252
I. B. Fesenko, “Adelic approach to the zeta function of arithmetic schemes in dimension two”, Mosc. Math. J., 8:2 (2008), 273–317
Gorchinskiy S., “Notes on the Biextension of Chow Groups”, Motives and Algebraic Cycles: a Celebration in Honour of Spencer J. Bloch, Fields Institute Communications, 56, 2009, 111–148
R. Ya. Budylin, “An adelic construction of Chern classes”, Sb. Math., 202:11 (2011), 1637–1659
S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarkhin, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, V. L. Popov, A. G. Sergeev, I. R. Shafarevich, “Aleksei Nikolaevich Parshin (on his 70th birthday)”, Russian Math. Surveys, 68:1 (2013), 189–197
S. V. Vostokov, “Shafarevich's paper “A general reciprocity law””, Sb. Math., 204:6 (2013), 781–800
R. Ya. Budylin, S. O. Gorchinskiy, “Intersections of adelic groups on a surface”, Sb. Math., 204:12 (2013), 1701–1711
Braunling O., “Geometric Two-Dimensional Ideles With Cycle Module Coefficients”, Math. Nachr., 287:17-18 (2014), 1954–1971
Camara A., “Locally Convex Structures on Higher Local Fields”, J. Number Theory, 143 (2014), 185–213
Ivan Fesenko, “Geometric adeles and the Riemann–Roch theorem for $1$-cycles on surfaces”, Mosc. Math. J., 15:3 (2015), 435–453
Gorchinskiy S., Rosly A., “a Polar Complex For Locally Free Sheaves”, Int. Math. Res. Notices, 2015, no. 10, 2784–2829
St. Petersburg Math. J., 27:6 (2016), 1003–1028
Sergey O. Gorchinskiy, Denis V. Osipov, “Continuous homomorphisms between algebras of iterated Laurent series over a ring”, Proc. Steklov Inst. Math., 294 (2016), 47–66
Oliver Braunling, Michael Groechenig, Jesse Wolfson, “Tate objects in exact categories (with an appendix by Jan Šťovíček and Jan Trlifaj)”, Mosc. Math. J., 16:3 (2016), 433–504
Braunling O., Groechenig M., Wolfson J., “Operator ideals in Tate objects”, Math. Res. Lett., 23:6 (2016), 1565–1631
Liu D., “Residues and duality on semi-local two-dimensional adeles”, J. Algebra, 448 (2016), 74–83
Liu D. Zhu Y., “Lca(2), Weil Index, and Product Formula”, Adv. Math., 329 (2018), 1088–1136
D. V. Osipov, “Adelic quotient group for algebraic surfaces”, St. Petersburg Math. J., 30:1 (2019), 111–122
D. V. Osipov, “Arithmetic surfaces and adelic quotient groups”, Izv. Math., 82:4 (2018), 817–836
A. N. Parshin, “The Mellin Transform and the Plancherel Theorem for the Discrete Heisenberg Group”, Proc. Steklov Inst. Math., 307 (2019), 174–192
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A. I. Madunts, “Mnozhestva skhodimosti mnogomernogo polnogo polya”, Voprosy teorii predstavlenii algebr i grupp. 35, Zap. nauchn. sem. POMI, 492, POMI, SPb., 2020, 125–133

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