### Abstract

This is a survey of results obtained by members of the St. Petersburg school of local number theory headed by S.V. Vostokov during the past decades. All these results hardly fit into the title of the paper, since they involve a large circle of ideas, which are applied to an even larger class of problems of modern number theory. The authors tried to cover at least a small part of them, namely, those related to the modern approach to explicit expressions of the Hilbert symbol for nonclassical formal modules in the one- and higher-dimensional cases and their applications in local arithmetic geometry and ramification theory.

Original language | English |
---|---|

Pages (from-to) | 242-264 |

Number of pages | 23 |

Journal | Vestnik St. Petersburg University: Mathematics |

Volume | 50 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jul 2017 |

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### Scopus subject areas

- Mathematics(all)

### Cite this

*Vestnik St. Petersburg University: Mathematics*,

*50*(3), 242-264. https://doi.org/10.3103/S1063454117030128

}

*Vestnik St. Petersburg University: Mathematics*, vol. 50, no. 3, pp. 242-264. https://doi.org/10.3103/S1063454117030128

**Explicit constructions and the arithmetic of local number fields.** / Vostokov, S. V.; Afanas’eva, S. S.; Bondarko, M. V.; Volkov, V. V.; Demchenko, O. V.; Ikonnikova, E. V.; Zhukov, I. B.; Nekrasov, I. I.; Pital’, P. N.

Research output

TY - JOUR

T1 - Explicit constructions and the arithmetic of local number fields

AU - Vostokov, S. V.

AU - Afanas’eva, S. S.

AU - Bondarko, M. V.

AU - Volkov, V. V.

AU - Demchenko, O. V.

AU - Ikonnikova, E. V.

AU - Zhukov, I. B.

AU - Nekrasov, I. I.

AU - Pital’, P. N.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - This is a survey of results obtained by members of the St. Petersburg school of local number theory headed by S.V. Vostokov during the past decades. All these results hardly fit into the title of the paper, since they involve a large circle of ideas, which are applied to an even larger class of problems of modern number theory. The authors tried to cover at least a small part of them, namely, those related to the modern approach to explicit expressions of the Hilbert symbol for nonclassical formal modules in the one- and higher-dimensional cases and their applications in local arithmetic geometry and ramification theory.

AB - This is a survey of results obtained by members of the St. Petersburg school of local number theory headed by S.V. Vostokov during the past decades. All these results hardly fit into the title of the paper, since they involve a large circle of ideas, which are applied to an even larger class of problems of modern number theory. The authors tried to cover at least a small part of them, namely, those related to the modern approach to explicit expressions of the Hilbert symbol for nonclassical formal modules in the one- and higher-dimensional cases and their applications in local arithmetic geometry and ramification theory.

KW - formal groups

KW - higher local fields

KW - local number fields

KW - reciprocity law

UR - http://www.scopus.com/inward/record.url?scp=85029154804&partnerID=8YFLogxK

U2 - 10.3103/S1063454117030128

DO - 10.3103/S1063454117030128

M3 - Article

AN - SCOPUS:85029154804

VL - 50

SP - 242

EP - 264

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -