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Abstract
The aim of this work is to provide an algebraic-geometric method to construct generalized local symbols on curves as morphisms of group schemes. From a closed point of a complete, irreducible, and nonsingular 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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ACKNOWLEDGMENT
The main results of the present article are part of the author's Ph.D. thesis. I would like to express my gratitude to my thesis advisor, Prof. Dr. José María Muñoz Porras, for his constant support and help with this work.
This work is partially supported by the DGI research contract no. MTM2009-11393 and Castilla y León Regional Government contract SA112A07.
Notes
Communicated by C. Pedrini.