Tagged Questions
3
votes
1answer
83 views
Characters being everywhere dense in the character group
Let $k$ be the completion of an algebraic number field at a prime divisor $\mathfrak{p}$. We note that $k$ is locally compact. Let $k^{+}$ be the additive group of $k$ which is a locally compact ...
5
votes
2answers
962 views
Local-Global Principle and the Cassels statement.
In a recent article I have read, i.e. " Lecture notes on elliptic curves ", Prof.Cassels remarks in page-110 that
There is not merely a local-global principle for curves of genus-$0$, but
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3
votes
1answer
124 views
Why are characters required to be continuous?
I learned from several places that in defining a character of a topological group $G$, we often require it to be continuous, i.e. $\omega:G\to \mathbb{C}^{\times}$ is a continuous group homomorphism. ...
