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Pablos Romo, Fernando 2025-03-05T12:08:06Z 2025-03-05T12:08:06Z 2006 Fernando Pablos Romo, 3-Cocycles, symbols and reciprocity laws on curves, Journal of Pure and Applied Algebra, Volume 205, Issue 1, 2006, Pages 94-116, ISSN 0022-4049, https://doi.org/10.1016/j.jpaa.2005.06.004. (https://www.sciencedirect.com/science/article/pii/S0022404905001416) 0022-4049 http://hdl.handle.net/10366/164060 10.1016/j.jpaa.2005.06.004 [EN]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 {·, ·, ·} and the symbol is a differentiated element of the cohomology class [{·, ·, ·}] ∈ 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. eng info:eu-repo/semantics/openAccess 3-cocycle Arithmetic symbols Reciprocity laws 3-Cocycles, symbols and reciprocity laws on curves info:eu-repo/semantics/article