Título
3-Cocycles, symbols and reciprocity laws on curves
Autor(es)
Palabras clave
3-cocycle
Arithmetic symbols
Reciprocity laws
Clasificación UNESCO
Fecha de publicación
2006
Editor
Elsevier
Citación
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)
Resumen
[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.
URI
ISSN
0022-4049
DOI
10.1016/j.jpaa.2005.06.004
Versión del editor
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