Abstract
We introduce a new approach for the study of two-dimensional symbols, F * × F * × F * → G , where F is a discrete valuation field and G is a commutative group. From central extensions of groups we obtain a three-cocycle { · , · , · } v F , v K ϕ and the symbol is a differentiated element of the cohomology class [ { · , · , · } v F , v K ϕ ] ∈ H 3 ( F * , G ) . Our construction generalizes well-known two-dimensional symbols, such as the Parshin symbol on a surface, and we offer a proof and a conjecture for reciprocity laws on curves related to these symbols.
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