Geodesic
Noncommutative reciprocity laws on algebraic surfaces: the case of tame ramification
Sbornik. Mathematics, Tome 204 (2013) no. 12, pp. 1797-1810 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove noncommutative reciprocity laws on an algebraic surface defined over a perfect field. These reciprocity laws establish that some central extensions of globally constructed groups split over certain subgroups constructed by points or projective curves on a surface. For a two-dimensional local field with a last finite residue field, the local central extension which is constructed is isomorphic to the central extension which comes from the case of tame ramification of the Abelian two-dimensional local Langlands correspondence suggested by Kapranov. Bibliography: 9 titles.
Keywords: central extensions, reciprocity laws.
Mots-clés : two-dimensional adèles, Picard groupoids 
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D. V. Osipov. Noncommutative reciprocity laws on algebraic surfaces: the case of tame ramification. Sbornik. Mathematics, Tome 204 (2013) no. 12, pp. 1797-1810. http://geodesic.mathdoc.fr/item/SM_2013_204_12_a4/

[1] D. Osipov, X. Zhu, “A categorical proof of the Parshin reciprocity laws on algebraic surfaces”, Algebra Number Theory, 5:3 (2011), 289–337 | DOI | MR | Zbl

[2] A. N. Parshin, “Local class field theory”, Proc. Steklov Inst. Math., 165 (1985), 157–185 | MR | Zbl

[3] D. V. Osipov, “The unramified two-dimensional Langlands correspondence”, Izv. Math., 77:4 (2013), 714–741 | DOI | DOI | Zbl

[4] M. M. Kapranov, “Analogies between the Langlands correspondence and topological quantum field theory”, Functional analysis on the eve of the 21st century, New Brunswick, NJ, 1993, v. 1, Progr. Math., 131, Birkhäuser, Boston, MA, 1995, 119–151 | MR | Zbl

[5] L. Breen, “Monoidal categores and multiextensions”, Compositio Math., 117:3 (1999), 295–335 | DOI | MR | Zbl

[6] L. Breen, “Bitorseurs et cohomologie non abélienne”, The Grothendieck Festschrift, v. I, Progr. Math., 86, Birkhäuser, Boston, MA, 1990, 401–476 | MR | Zbl

[7] D. V. Osipov, “$n$-dimensional local fields and adeles on $n$-dimensional schemes”, Surveys in contemporary mathematics, London Math. Soc. Lecture Note Ser., 347, Cambridge Univ. Press, Cambridge, 2008, 131–164 | MR | Zbl

[8] D. Osipov, “Adeles on $n$-dimensional schemes and categories $C_n$”, Internat. J. Math., 18:3 (2007), 269–279 | DOI | MR | Zbl

[9] J.-L. Brylinski, D. A. McLaughlin, “Non-commutative reciprocity laws associated to finite groups”, Operads: Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995), Contemp. Math., 202, Amer. Math. Soc., Providence, RI, 1997, 421–438 | DOI | MR | Zbl