All Questions

I'm looking for a reference for the following facts from global class field theory that I found without proofs. I will state them as questions, just in case I get the statement wrong. We fix $K$ a ...

I’m studying Iwasawa theory and I meet some questions Thanks a lot for your help. Q_1: About terminology $p$-extension. I find many reference use maximal $p$-extension or maximal abelian p-extension ...

I am trying to undesrtand the analogy between the Euler systems over abelian extensions of the rationals and the Euler systems over abelian extensions of imaginary quadratic fields. As Soogil Seo ...

If $f : X\to V$ is a smooth proper map of smooth schemes, what are the global sections of $R^if_{fppf, *}\mu_p$ $R^if_{fppf, *}\mathbb{G}_{\rm m}$ I was reading Milne's book "Arithmetic duality", ...

$\DeclareMathOperator\trdeg{trdeg} \DeclareMathOperator\Frac{Frac} $ Let $k$ be an algebraically closed field of characteristic $0$ and $K$ a function field over $k$. let $(A, \mathfrak{m}_A)$ a ...

Let $k$ be a number field, let $\bar k \subseteq \mathbb{C}$ be a fixed algebraic closure of $k$, and let $S$ be the set of infinite primes of $k$. Denote by $k_S$ the maximal extension of $k$ inside $...