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First of all, I realized that I had made a big mistake. The Galois extension $k_{n}/k^{+}$ is abelian (since it is a composite of $k/k^{+}$ and $\mathbb{B}_{m}/\mathbb{Q}$ for some m.) hence the compl …

I'm currently reading the paper "On a Certain l-Adic Reprersentation" written by Ralph Greenberg.(Inventiones 1973) And I'm stuck with a proof of the Proposition 2. Here $k$ is a totally imaginary ab …

I'm currently reading the book "Galois theory of $p$-extensions" by Helmut Koch. There, we calculate the cohomological dimension of the galois group $G(K/k)$ where $K$ is the maximal (normal) $p$-ext …

I'm reading the paper of Cohen and Martinet 'Etude heuristique des groups de classes'. In the section 6, for an central idempotent $e$ of $\mathbb{Q}[\Gamma]$ and a prime $p$, the 'goodness' of $p$ is …

I've wanted to understand the concept of the Dualizing module in the theory of Galois Cohomology. There are many references on it and of them all Neukirch's Cohomology of Number Fields seems to be ela …

I'm currently reading a paper of Georges Gras on the Reflection Principle. The paper uses some theorems about orders (ring theory) from the book "Maximal Orders" by Reiner. I find the book interesting …

I'm currently interested in the cardinality of the set of values of a polynomial over a finite field. I found a paper Saburo Uchiyama, Sur le Nombre des Valeurs Distinctes d'un Polynome a Coeffi …

Nowadays there are many papers on the number theory using heuristics. I have read some of them. But I have no clear understanding of the Bayesian Probability(subjective probability). The concept of us …

I'm currently trying to understand the Brauer-Kuroda formula. Although there are many recent papers on the formula but they seem to be purely algebraic. They say that original analytic approach is m …

I'm currently interested in finding good upper bounds for the relative class numbers of non-abelian CM-fields. So I'm looking for some references to learn the techniques that can be useful. So far, I …