Generalized Fesenko reciprocity map
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- by K. I. Ikeda and E. Serbest
- St. Petersburg Math. J. 20 (2009), 593-624
- DOI: https://doi.org/10.1090/S1061-0022-09-01063-2
- Published electronically: June 1, 2009
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Abstract:
The paper is a natural continuation and generalization of the works of Fesenko and of the authors. Fesenko’s theory is carried over to infinite APF Galois extensions $L$ over a local field $K$ with a finite residue-class field $\kappa _K$ of $q=p^f$ elements, satisfying $\pmb {\mu }_p(K^{\mathrm {sep}})\subset K$ and $K\subset L\subset K_{\varphi ^d}$, where the residue-class degree $[\kappa _L:\kappa _K]$ is equal to $d$. More precisely, for such extensions $L/K$ and a fixed Lubin–Tate splitting $\varphi$ over $K$, a $1$-cocycle \begin{equation*} \pmb {\Phi }_{L/K}^{(\varphi )}:\mathrm {Gal}(L/K)\rightarrow K^\times /N_{L_0/K}L_0^\times \times U_{\widetilde {\mathbb X}(L/K)}^\diamond /Y_{L/L_0}, \end{equation*} where $L_0=L\cap K^{nr}$, is constructed, and its functorial and ramification-theoretic properties are studied. The case of $d=1$ recovers the theory of Fesenko.References
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Bibliographic Information
- K. I. Ikeda
- Affiliation: Department of Mathematics, Yeditepe University, 26 Aǧustos Yerleşimi, İnönü Mah., Kayışdaǧı Cad., 34755 Kadıköy, Istanbul, Turkey
- Email: ilhan.ikeda@yeditepe.edu.tr
- E. Serbest
- Affiliation: Gümüş Pala Mahallesi, Gümüş Sok., Öz Aksu Sitesi, C-2/39, 34160 Avcılar, Istanbul, Turkey
- Email: erols73@yahoo.com
- Received by editor(s): October 20, 2007
- Published electronically: June 1, 2009
- © Copyright 2009 American Mathematical Society
- Journal: St. Petersburg Math. J. 20 (2009), 593-624
- MSC (2000): Primary 11S37
- DOI: https://doi.org/10.1090/S1061-0022-09-01063-2
- MathSciNet review: 2473746