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I'm now on a research about the Iwasawa $\lambda$-invariants of the cyclotomic $\mathbb{Z}_p$-extensions of number fields. And it happens that the cyclotomic $\mathbb{Z}_3$-extension of $\mathbb{Q}(\s …

Now I'm reading the paper of Friedrich Roesler on the representation theory of Schur-Rings with the title 'Darstellungstheorie von Schur-Algebren' (Math Z 1972). My goal is to understand algebraic the …

I'm now interested in classifying the indecomposable modules over $\mathbb{Z}/p^{2}\mathbb{Z}[\mathbb{Z}/p\mathbb{Z}]$ : the group ring of $\mathbb{Z}/p\mathbb{Z}$ over the ring $\mathbb{Z}/p^{2}\math …

I am searching for a reference on the Gröbner-Shirshov algorithm specifically for free restricted Lie algebras. I have already consulted the textbook by Bokut et al (Gröbner–Shirshov Bases Normal Form …

I'm interested in the paper of Jan Saxl "The Complex Characters of the Symmetric Groups that Remain Irreducible in Subgroups". I have only (not yet enough!) standard background on the representation t …

I'm currently studying Iwasawa theory. 1) There are many $\mathbb{Z}_p$-modules on which some Galois groups act. So I often face some facts on the group representation over local fields or p-adic int …

I've been reading the book 'Cohomology of Number Fields' for years. But I couldn't check the commutativity of the diagram on page 126 until now. So I ask for help. The diagram is induced by taking …

I've been wanted to learn some basic theories of the (non-semisimple) representation of the finite group over a finite field. I have been guessing that the materials might be contained in the books on …

I'm currently reading the paper of Henri Cohen & Jacques Martinet "Etude heuristique des groupes de classes des corps de nombres" On the 2nd section, they recall some facts on valuations, completions …

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 want to know whether there are any research on the orbits of the action of a subgroup by conjugation on the whole group, when the group is finite. (Especially whole symmetric group.) I'm especially …

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 …

While reading a paper, I found a mentioning that for an extension $1 \rightarrow H \rightarrow G \rightarrow N \rightarrow 1$ of pro-$p$ groups, the Euler–Poincaré characteristics $\chi(H)$, $\chi(G)$ …