Results 61 to 70 of about 7,243 (134)

The degrees of the cyclotomic extension fields

Linear Algebra and its Applications, 1993
The following question is investigated: ``Suppose \(r\) and \(s\) are relatively prime positive integers and \(\xi_ r\), \(\xi_ s\), \(\xi_{rs}\) primitive roots of unity. When for positive integers \(a\), \(b\) and \(c\) is there a field \(K\) of characteristic zero with \(| K(\xi_{rs}): K|=a\), \(| K(\xi_ r): K| =b\), and \(| K(\xi_ s):K| =c ...
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On the structure of the Galois group of the maximal pro-$p$ extension with restricted ramification over the cyclotomic $\mathbb{Z}_p$-extension

, 2018
Let $k_\infty$ be the cyclotomic $\mathbb{Z}_p$-extension of an algebraic number field $k$. We denote by $S$ a finite set of prime numbers which does not contain $p$, and $S(k_\infty)$ the set of primes of $k_\infty$ lying above $S$. In the present paper,
Itoh, Tsuyoshi
core  

Class numbers in cyclotomic Z_p-extensions

, 2014
22 pages.
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Galois groups of some iterated polynomials over cyclotomic extensions [PDF]

Archiv der Mathematik, 2017
We strengthen the main result to all non-Wieferich ...
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Unit groups of some multiquadratic number fields and 2-class groups. [PDF]

Period Math Hung, 2022
Chems-Eddin MM.
europepmc   +1 more source

Torsion of abelian varieties, Weil classes and cyclotomic extensions [PDF]

Mathematical Proceedings of the Cambridge Philosophical Society, 1999
Let $K$ be a field finitely generated over the field of rational numbers, $K(c)$ the extension of $K$ obtained by adjoining all roots of unity, $L$ an infinite Galois extension of $K$, $X$ an abelian variety defined over $K$. We prove that under certain conditions on $X$ and $K$ the existence of infinitely many L-rational points of finite order on $X ...
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Modularity of PGL₂(𝔽p)-representations over totally real fields. [PDF]

Proc Natl Acad Sci U S A, 2021
Allen PB, Khare CB, Thorne JA.
europepmc   +1 more source

A Density of Ramified Primes. [PDF]

Res Number Theory, 2022
Chan S, McMeekin C, Milovic D.
europepmc   +1 more source

Another look at rational torsion of modular Jacobians. [PDF]

Proc Natl Acad Sci U S A, 2022
Ribet KA, Wake P.
europepmc   +1 more source

Zariski density of crystalline points. [PDF]

Proc Natl Acad Sci U S A, 2023
Böckle G, Iyengar A, Paškūnas V.
europepmc   +1 more source