Geodesic
An explicit formula for the Hilbert symbol for Honda
Sbornik. Mathematics, Tome 194 (2003) no. 2, pp. 165-197 Cet article a éte moissonné depuis la source Math-Net.Ru

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Based on the pairing on Cartier curves explicitly constructed in the previous paper of the authors, an explicit formula for the Hilbert symbol is constructed in a multidimensional local field of characteristic zero with residue field of positive characteristic on the formal module of a one-dimensional Honda formal group. In the proof a Shafarevich basis on the formal module is constructed, and so-called integer $\mu$-modules in two-dimensional local rings of a special form ( $\mu$-rings) are studied. 
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S. V. Vostokov; F. Lorenz. An explicit formula for the Hilbert symbol for Honda. Sbornik. Mathematics, Tome 194 (2003) no. 2, pp. 165-197. http://geodesic.mathdoc.fr/item/SM_2003_194_2_a0/

[1] Lorenz F., Vostokov S. V., “Honda groups and explicit pairing on the modules of Cartier curves”, Algebraic number theory and algebraic geometry, eds. S. Vostokov, Yu. Zarhin, Amer. Math. Soc., Providence, RI, 2002, 143–170 | MR | Zbl

[2] Abrashkin A. V., “Yavnaya formula dlya simvola Gilberta formalnoi gruppy Khondy nad vektorami Vitta”, Izv. RAN. Ser. matem., 61:3 (1997), 3–56 | MR | Zbl

[3] Vostokov S. V., Demchenko O. V., “Yavnaya formula dlya simvola Gilberta formalnykh grupp Khondy”, Zapiski nauchn. sem. POMI, 272, 2000, 86–128 | MR | Zbl

[4] Fesenko I., Vostokov S., Local fields and their extensions: a constructive approach, Transl. Math. Monogr., 121, Amer. Math. Soc., Providence, RI, 1993 | MR | Zbl

[5] Vostokov S. V., “Explicit formulas for the Hilbert symbol”, Invitation to higher local fields. Geom. Topol. Monogr., 3 (2000), 81–90 | DOI | MR

[6] Vostokov S. V., Zhukov I. B., Fesenko I. B., “K teorii mnogomernykh lokalnykh polei. Metody i konstruktsii”, Algebra i analiz, 2:4 (1990), 91–118 | MR | Zbl

[7] Honda T., “On the theory of commutative formal groups”, J. Math. Soc. Japan, 22 (1970), 213–243 | MR

[8] Demchenko O. V., “Novoe sootnoshenie mezhdu formalnymi gruppami Lyubina–Teita i formalnymi gruppami Khondy”, Algebra i analiz, 10:5 (1998), 77–84 | MR | Zbl

[9] Parshin A. N., “Polya klassov i algebraicheskaya $K$-teoriya”, UMN, 30:1 (1975), 253–254 | MR | Zbl

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

[11] Kato K., “A generalisation of local class field theory by using $K$-groups. I”, J. Fac. Sci. Univ. Tokyo Sect. IA, 26 (1979), 303–376 ; “II”, J. Fac. Sci. Univ. Tokyo Sect. IA, 27 (1980), 603–683 | MR | Zbl | MR | Zbl

[12] Benua D. G., Vostokov S. V., “Normennoe sparivanie v formalnykh gruppakh i predstavleniya Galua”, Algebra i analiz, 2:6 (1990), 69–97 | MR | Zbl

[13] Demchenko O. V., “Formalnye gruppy Khondy: arifmetika gruppy tochek”, Algebra i analiz, 12:1 (2000), 132–149 | MR | Zbl

[14] Kolyvagin V. A., “Formalnye gruppy i simvol normennogo vycheta”, Izv. AN SSSR. Ser. matem., 43 (1979), 1054–1120 | MR | Zbl

[15] Vostokov S. V., “Yavnaya konstruktsiya teorii polei klassov dlya mnogomernykh lokalnykh polei”, Izv. AN SSSR. Ser. matem., 49 (1985), 283–308 | MR