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9
votes
1answer
725 views

Weil reciprocity vs Artin reciprocity

This is probably an easy question for the experts: Given two rational functions $f$, $g$ on a non-singular projective algebraic curve X (over an algebraically closed field $k$) and $p \in X$, one ...
8
votes
0answers
392 views

Hilbert symbol and Weil index, beyond the quadratic case?

Let $F$ be a local nonarchimedean field. Let $n$ be a positive integer for which the group $\mu_n(F)$ of $n^{th}$ roots of unity in $F$ has order $n$. Let $\epsilon: \mu_n(F) \rightarrow C^\times$ ...