The hilbert-symbol tag has no wiki summary.

**1**

vote

**0**answers

109 views

### Skew symmetry for the Hilbert symbol

Let $K$ be a local field containing the group $\mu_n$ of $n$th roots of 1 and the $\theta_K:K^*\to G_K^{ab}$ be the reciprocity map. The we know that the Hilbert symbol $$K^*\times K^*\to \mu_n$$ ...

**9**

votes

**1**answer

845 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

**0**answers

413 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 $\epsilon: \mu_n(F) \rightarrow C^\times$ ...