|
This article is cited in 40 scientific papers (total in 41 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.
 Full text:
PDF file (3279 kB)
References:
PDF file
HTML file
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
\Bibitem{Par76}
\by A.~N.~Parshin
\paper On the arithmetic of two-dimensional schemes. I.~Distributions and residues
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 4
\pages 736--773
\mathnet{http://mi.mathnet.ru/izv2201}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=419458}
\zmath{https://zbmath.org/?q=an:0358.14012}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 4
\pages 695--729
\crossref{https://doi.org/10.1070/IM1976v010n04ABEH001810}
Linking options:
http://mi.mathnet.ru/eng/izv2201 http://mi.mathnet.ru/eng/izv/v40/i4/p736
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 (2019), 111–122
-
D. V. Osipov, “Arithmetic surfaces and adelic quotient groups”, Izv. Math., 82:4 (2018), 817–836
|
| Number of views: |
| This page: | 839 | | Full text: | 253 | | References: | 36 | | First page: | 3 |
|
Terms of Use