A generalized contou-carrère symbol and its reciprocity laws in higher dimensions

Abstract: We generalize Contou-Carr`ere symbols to higher dimensions. To an (n + 1)-tuple f0, . . . , fn ∈ A((t1)) · · · ((tn))×, where A denotes an algebra over a field k, we associate an element (f0, . . . , fn) ∈ A×, extending the higher tame symbol for k = A, and earlier constructions for n = 1 by Contou-Carr`ere, and n = 2 by Osipov–Zhu. It is based on the concept of higher commutators for central extensions by spectra. Using these tools, we describe the higher Contou-Carr`ere symbol as a composition of boundary maps in algebraic K- theory, and prove a version of Parshin–Kato reciprocity for higher Contou- Carr`ere symbols

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch
• Notes: Transactions of the American Mathematical Society. Series B. - 8, 23 (2021) , 679-753, ISSN: 2330-0000

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Freiburg
• (who): Universität
• (when): 2024
• Creator: Braunling, Oliver ; Groechenig, Michael ; Wolfson, Jesse

Further information

• DOI: 10.1090/btran/81
• URN: urn:nbn:de:bsz:25-freidok-2485524
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 10:58 AM CEST