Geometric Construction of Generalized Local Symbols on Algebraic Curves
Fernando Pablos Romo
Abstract
The aim of this work is to provide a construction of generalized local symbols on algebraic curves as morphisms of group schemes. From a closed point of a complete, irreducible and non-singular curve C over a perfect field k as the only data, using theta groups over Picard schemes of curves, we offer a geometric construction that allows us to define generalizations of the tame symbol and the Hilbert norm residue symbol.
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