All Questions

Let $K_\infty/\mathbb{Q}$ denote the $\hat{\mathbb{Z}}$-extension of $\mathbb{Q}$. Then for each $n\geq1$, $K_\infty$ has a unique subfield $K_n$ of degree $n$ over $\mathbb{Q}$. The fields $K_n$ are ...

I recently learned Sharifi's conjecture in this article by F.Takako and K.Kato. According to my understanding, this conjecture states that (the conjugation invariant) of the projective limit $\...

Let $p>2$ be a prime, $\zeta$ a primitive $p$th root of unity, and $m >0$ a square-free integer such that $m \not\equiv 3 \mod 4$ and $\gcd(m,p)=1$. Let $\chi$ be the imaginary quadratic ...

1.Let $p$ be an odd prime number. Is there a classification of cyclotomic fields of the form $\mathbb{Q}(\zeta_p)$ with class number 1? 2.Is there such a classification for general cyclotomic fields $...