Geodesic
The Hensel--Shafarevich canonical basis in Honda formal modules
Čebyševskij sbornik, Tome 21 (2020) no. 1, pp. 368-373.

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In this paper, we construct Hensel–Shafarevich generating set in Honda formal modules over a higher dimensional field. Later, that should allow us to compute Hilbert symbol in this case.
Keywords: formal groups, formal modules. 
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S. V. Vostokov; R. P. Vostokova; E. V. Ikonnikova. The Hensel--Shafarevich canonical basis in Honda formal modules. Čebyševskij sbornik, Tome 21 (2020) no. 1, pp. 368-373. http://geodesic.mathdoc.fr/item/CHEB_2020_21_1_a24/

[1] Ivan B. Fesenko, S. V. Vostokov, Local fields and their extensions, AMS Bookstore, 2002 | MR

[2] M. Hazewinkel, Formal Groups and Applications, Pure Appl. Math., 78, Academic Press, New York, 1978 | MR | Zbl

[3] J. Lubin, J. Tate, “Formal complex multiplication in local fields”, Annals of Mathematics. Second Series, 81, 1965, 380–387 | DOI | MR | Zbl

[4] M.V. Bondarko, S.V. Vostokov, F. Lorenz, “The Hilbert pairing for formal groups over $\sigma$-rings”, J. Math. Sci. (N. Y.), 134:6 (2006), 2445–2476 | DOI | MR | Zbl

[5] S. V. Vostokov, “A norm pairing in formal modules”, Math. USSR-Izv., 15:1 (1980), 25–51 | DOI | MR | Zbl

[6] S. V. Vostokov, “Canonical basis of Hensel-Shafarevich in complete discrete valuation fields”, J. Math. Sci. (N. Y.), 188:5 (2013), 570–581 | DOI | MR | Zbl

[7] S. V. Vostokov, I. L. Klimovitskii, “Primary Elements in Formal Modules”, Proc. Steklov Inst. Math., 282, suppl. 1 (2013), S140–S149 | DOI | MR | Zbl

[8] D. G. Benois, S. V. Vostokov, “Norm pairing in formal groups and Galois representations”, Leningrad Math. J., 2:6 (1991), 1221–1249 | MR | Zbl

[9] O. V. Demchenko, “Formal Honda groups: the arithmetic of the group of points”, St. Petersburg Math. J., 12:1 (2001), 101–115 | MR | Zbl

[10] O. V. Demchenko, “New relationships between formal Lubin-Tate groups and formal Honda groups”, St. Petersburg Math. J., 10:5 (1999), 785–789 | MR | Zbl

[11] S. S. Afanas'eva, R. P. Vostokova, “Logarithms of formal A-modules in the case of small ramification”, St. Petersburg Math. J., 27:6 (2016), 863–868 | DOI | MR | Zbl

[12] Ikonnikova E.V., Shaverdova E.V., “The Shafarevich basis in higher dimensional local fields”, Journal of Mathematical Sciences (United States), 202:3 (2014), 410–421 | DOI | MR | Zbl

[13] Ikonnikova E.V., “The Hensel-Shafarevich canonical basis in Lubin-Tate formal modules”, Journal of Mathematical Sciences (United States), 219:3 (2016), 462–472 | DOI | MR | Zbl

[14] Afanaseva S.S., Ikonnikova E.V., “Arithmetic of $\pi_0$-critical module”, Lobachevskii Journal of Mathematics, 38:1 (2017), 131–136 | DOI | MR | Zbl