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oai:gredos.usal.es:10366/1640492025-05-06T07:43:38Zcom_10366_4146com_10366_4055com_10366_3946com_10366_3823col_10366_4147

Pablos Romo, Fernando 2025-03-05T09:45:11Z 2025-03-05T09:45:11Z 2003 Pablos Romo, F. (2003). A Note on Steinberg Symbols on Algebraic Curves. Communications in Algebra, 31(2), 981–990. https://doi.org/10.1081/AGB-120017354 0092-7872. 1532-4125 http://hdl.handle.net/10366/164049 10.1081/AGB-120017354 [EN]The aim of this paper is to provide a method for defining Steinberg symbols on a complete algebraic curve over a perfect field k from the commutator of a certain extension of groups. This extension is associated with a group morphism ϕ : k* → G. With this definition the reciprocity law is a consequence of the finiteness of the cohomology groups H^0(C, 𝒪_C ) and H^1(C, 𝒪_C ). Using this method, Hilbert's norm residue symbol on an algebraic curve and the symbol (a, b)_v for the field ℚ_p (n = 2) can be defined. eng info:eu-repo/semantics/embargoedAccess Steinberg symbol Algebraic curve Reciprocity law A Note on Steinberg Symbols on Algebraic Curves info:eu-repo/semantics/article