chebЧебышевский сборникChebyshevskii Sbornik2226-8383Tula State Lev Tolstoy Pedagogical University10.22405/2226-8383-2025-26-4-37-70cheb-2069Research ArticleСтатьиArticleЯвные законы взаимности в теории локальных полейExplicit reciprocity laws in the theory of local fieldsБенуаДенис ГеоргиевичBenoisDenis Georgievichdenis.benois@math.u-bordeaux.frУниверситет БордоФранцияUniversit´e de BordeauxFrance2025291220252643770Copyright © Бенуа Д.Г., 20252025Бенуа Д.Г.Benois D.G.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.chebsbornik.ru/jour/article/view/2069

В этой обзорной статье рассматриваются различные подходы к явному описанию символа Гильберта и их обобщения на 𝑝-адические представления в рамках 𝑝-адической теории Ходжа.

This paper surveys different approaches to explicit formulas for the Hilbert symbol and their generalizations to 𝑝-adic representations in terms of 𝑝-adic Hodge theory.

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The authors declare that there are no conflicts of interest present.