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This tag is used if a reference is needed in a paper or textbook on a specific result.

15 votes
6 answers
2k views

Any shortcuts to understanding the properties of the Riemannian manifolds which are used in ...

I'm now attending a reading seminar on the algebraic topology. The seminar treats the book of Bott & Tu (Differential Forms in Algebraic Topology) and Milnor (Characteristic Classes). In those books, …
gualterio's user avatar
  • 1,013
8 votes
0 answers
265 views

A diagram in the proof of Theorem 2.5.5 of 'Cohomology of Number Fields' and the Tate Spectr...

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 …
gualterio's user avatar
  • 1,013
6 votes
0 answers
99 views

Computer program for free restricted Lie polynomial

I am conducting numerical experiments involving the Gröbner–Shirshov Basis for restricted Lie algebras. At each step of the computation, I need to work with restricted Lie polynomials. Specifically, I …
gualterio's user avatar
  • 1,013
5 votes
0 answers
346 views

Modern reference for Andre Weil's 'Sur les courbes algébriques et les variétés qui s'en dédu...

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 …
gualterio's user avatar
  • 1,013
5 votes
1 answer
246 views

Classifying indecomposable modules over $\mathbb{Z}/p^{2}\mathbb{Z}[\mathbb{Z}/p\mathbb{Z}]$

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 …
gualterio's user avatar
  • 1,013
4 votes
1 answer
496 views

I want to know the name of or any references for a matrix in the book "The representation th...

$\DeclareMathOperator{\Ind}{\operatorname{Ind}}$I'm reading "The representation theory of the symmetric groups" written by Gordon James. I found the matrix $B$ in the chapter 6 ("The character table o …
gualterio's user avatar
  • 1,013
3 votes
1 answer
190 views

English reference for the Brauer-Kuroda formula

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 …
gualterio's user avatar
  • 1,013
3 votes
0 answers
95 views

Study of relative class number of 'non-abelian' CM field by using L-functions

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 …
gualterio's user avatar
  • 1,013
3 votes
2 answers
420 views

Is there any simple formula for the character of $S_{n}$ represented by the set of $k$-tuple...

I'm interested in the representation theory of symmetric groups. I'm now trying to search for the formula for the characters of $\Omega^{k}$, the set of $k$-tuple of elements of $\Omega$ a set of $n$ …
gualterio's user avatar
  • 1,013
3 votes
0 answers
115 views

Reference for the Netto's theorem on the permutation groups which was mentioned in the paper...

I'm trying to read 'Uber die Charaktere der mehrfach transitiven Gruppen' written by Frobenius. There he mentioned some theorems of Netto. I'm depending on the Google translator. and the translation …
gualterio's user avatar
  • 1,013
2 votes
0 answers
97 views

Is there any good reference on the Bayesian view that can be helpful for reading papers on t...

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 …
gualterio's user avatar
  • 1,013
2 votes
0 answers
371 views

Is there a roadmap to learning representation theory of finite group over finite field?

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 …
gualterio's user avatar
  • 1,013
1 vote
0 answers
184 views

The Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb{Z}_3$-extension of $\mathbb{Q}(\s...

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 …
gualterio's user avatar
  • 1,013
1 vote
1 answer
142 views

Valuation theory on semisimple algebras used in the paper of Cohen-Martinet: reference request

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 …
gualterio's user avatar
  • 1,013
1 vote
0 answers
89 views

Is there any English reference for the paper 'Darstellungstheorie von Schur-Algebren' writte...

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 …
gualterio's user avatar
  • 1,013

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