Geodesic
Central extensions and reciprocity laws on algebraic surfaces
Sbornik. Mathematics, Tome 196 (2005) no. 10, pp. 1503-1527 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Reciprocity laws on algebraic surfaces are proved for a certain integer-valued symbol. The interpretation of this symbol as the commutator of liftings of elements in a central extension of a certain group is used in the proof. 
@article{SM_2005_196_10_a4,
     author = {D. V. Osipov},
     title = {Central extensions and reciprocity laws on algebraic surfaces},
     journal = {Sbornik. Mathematics},
     pages = {1503--1527},
     year = {2005},
     volume = {196},
     number = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_10_a4/}
}
TY  - JOUR
AU  - D. V. Osipov
TI  - Central extensions and reciprocity laws on algebraic surfaces
JO  - Sbornik. Mathematics
PY  - 2005
SP  - 1503
EP  - 1527
VL  - 196
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/SM_2005_196_10_a4/
LA  - en
ID  - SM_2005_196_10_a4
ER  - 
%0 Journal Article
%A D. V. Osipov
%T Central extensions and reciprocity laws on algebraic surfaces
%J Sbornik. Mathematics
%D 2005
%P 1503-1527
%V 196
%N 10
%U http://geodesic.mathdoc.fr/item/SM_2005_196_10_a4/
%G en
%F SM_2005_196_10_a4
D. V. Osipov. Central extensions and reciprocity laws on algebraic surfaces. Sbornik. Mathematics, Tome 196 (2005) no. 10, pp. 1503-1527. http://geodesic.mathdoc.fr/item/SM_2005_196_10_a4/

[1] Parshin A. N., “Lokalnaya teoriya polei klassov”, Trudy MIAN, 165, 1984, 143–170 | MR | Zbl

[2] Beilinson A. A., “Vychety i adeli”, Funkts. analiz i ego prilozh., 14:1 (1980), 44–45 | MR | Zbl

[3] Fimmel T., Parshin A. N., Introduction to higher adelic theory, Preprint, Steklov Mathematical Institute, M., 1999 | MR

[4] Parshin A. N., “Chern classes, adeles and $L$-functions”, J. Reine Angew Math., 341 (1983), 174–192 | MR | Zbl

[5] Parshin A. N., “K arifmetike dvumernykh skhem. I. Raspredeleniya i vychety”, Izv. AN SSSR Ser. matem., 40:4 (1976), 736–773 | MR | Zbl

[6] Kapranov M. M., Semiinfinite symmetric powers, E-print: math.QA/0107089

[7] Tate J., “Residues of differentials on curves”, Ann. Sci. École Norm. Sup. (4), 1 (1968), 149–159 | MR | Zbl

[8] Arbarello E., De Concini C., Kac V. G., “The infinite wedge representation and the reciprocity law for algebraic curves”, Theta functions, Proc. 35th Summer Res. Inst. Bowdoin Coll. (Brunswick, ME, 1987), Proc. Sympos. Pure Math., 49, Amer. Math. Soc., Providence, RI, 1989, 171–190 | MR

[9] Brylinski J.-L., “Central extensions and reciprocity laws”, Cahiers Topologie Géom. Differéntielle Catég., 38:3 (1997), 193–215 | MR | Zbl

[10] Pablos Romo F., “On the tame symbol of an algebraic curve”, Comm. Algebra, 30:9 (2002), 4349–4368 | DOI | MR | Zbl

[11] Burbaki N., Kommutativnaya algebra, Mir, M., 1971 | MR

[12] Lefschetz S., Algebraic topology, Amer. Math. Soc. Colloq. Publ., 27, Amer. Math. Soc., New York, 1942 | MR | Zbl

[13] Beilinson A. A., “How to glue perverse sheaves”, $K$-theory, arithmetic and geometry (Moscow Univ. 1984–86), Lecture Notes in Math., 1289, Springer-Verlag, Berlin, 1987, 42–51 | MR

[14] Yekutieli A., An explicit construction of the Grothendieck residue complex. With an appendix by Pramathanath Sastry, Astérisque, 208, Soc. Math. France, Paris, 1992 | MR | Zbl

[15] Lomadze V. G., “Ob indekse peresecheniya divizorov”, Izv. AN SSSR. Ser. matem., 44 (1980), 1120–1130 | MR | Zbl

[16] Huber A., “On the Parshin–Beilinson adeles for schemes”, Abh. Math. Sem. Univ. Hamburg, 61 (1991), 249–273 | DOI | MR | Zbl

[17] Khartskhorn R., Algebraicheskaya geometriya, Mir, M., 1981 | MR | Zbl

[18] Atya M., Makdonald I., Vvedenie v kommutativnuyu algebru, Mir, M., 1972 | MR

[19] Osipov D. V., “Sootvetstvie Krichevera dlya algebraicheskikh mnogoobrazii”, Izv. RAN. Ser. matem., 65:5 (2001), 91–128 | MR | Zbl