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# On $n$-Dimensional Steinberg Symbols

The aim of this work is to provide a new approach for constructing $n$-dimensional Steinberg symbols on discrete valuation fields from $(n+1)$-cocycles and to study reciprocity laws on curves related to these symbols.
 MSC Classifications: 19F15 - Symbols and arithmetic [See also 11R37] 19D45 - Higher symbols, Milnor $K$-theory 19C09 - Central extensions and Schur multipliers