An explicit reciprocity law associated to some finite coverings of algebraic curves. (English) Zbl 1420.19006
In the previous paper [Trans. Am. Math. Soc. 360, No. 7, 3473–3492 (2008; Zbl 1194.14037)] the first two authors proved the existence of a generalized abstract reciprocity law for reductive groups defined over the function field of a smooth curve. In the current paper, the authors develop new reciprocity law associated with finite coverings of algebraic currves. They also provide specific explicit examples which demonstrate that their non-commutative reciprocity law is not equivalent to the Weil reciprocity law.
Reviewer: Piotr Krasoń (Szczecin)
MSC:
| 19F15 | Symbols and arithmetic (\(K\)-theoretic aspects) |
| 14H05 | Algebraic functions and function fields in algebraic geometry |
Citations:
Zbl 1194.14037References:
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