اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Other Group of as Galois Extension
206
0
0.0
(
0
)
تأليف
Lex E. Renner
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $ksubseteq K$ be a finite Galois extension of fields with Galois group $G$. Let $mathscr{G}$ be the automorphism $k$-group scheme of $K$. We construct a canonical $k$-subgroup scheme $underline{G}subsetmathscr{G}$ with the property that $Spec_k(K)$ is a $k$-torsor for $underline{G}$. $underline{G}$ is a constant $k$-group if and only if $G$ is abelian, in which case $G=underline{G}$.
قيم البحث
اقرأ أيضاً
Quantization is studied from a viewpoint of field extension. If the dynamical fields and their action have a periodicity, the space of wave functions should be algebraically extended `a la Galois, so that it may be consistent with the periodicity. Th
is was pointed out by Y. Nambu three decades ago. Having chosen quantum mechanics (one dimensional field theory), this paper shows that a different Galois extension gives a different quantization scheme. A new scheme of quantization appears when the invariance under Galois group is imposed as a physical state condition. Then, the normalization condition appears as a sum over the product of more than three wave functions, each of which is given for a different root adjoined by the field extension.
In this paper we show an explicit polynomial in Q[x] that has Galois group SL2(F16), filling in a gap in the tables of Juergen Klueners and Gunther Malle. The computation of this polynomial uses modular forms and their Galois representations.
The arboreal Galois group of a polynomial $f$ over a field $K$ encodes the action of Galois on the iterated preimages of a root point $x_0in K$, analogous to the action of Galois on the $ell$-power torsion of an abelian variety. We compute the arbore
al Galois group of the postcritically finite polynomial $f(z) = z^2 - 1$ when the field $K$ and root point $x_0$ satisfy a simple condition. We call the resulting group the arithmetic basilica group because of its relation to the basilica group associated with the complex dynamics of $f$. For $K=mathbb{Q}$, our condition holds for infinitely many choices of $x_0$.
We study the relationship between potential equivalence and character theory; we observe that potential equivalence of a representation $rho$ is determined by an equality of an $m$-power character $gmapsto Tr(rho(g^m))$ for some natural number $m$. U
sing this, we extend Faltings finiteness criteria to determine the equivalence of two $ell$-adic, semisimple representations of the absolute Galois group of a number field, to the context of potential equivalence. We also discuss finiteness results for twist unramified representations.
For positive integers $n$, the truncated binomial expansions of $(1+x)^n$ which consist of all the terms of degree $le r$ where $1 le r le n-2$ appear always to be irreducible. For fixed $r$ and $n$ sufficiently large, this is known to be the case. W
e show here that for a fixed positive integer $r e 6$ and $n$ sufficiently large, the Galois group of such a polynomial over the rationals is the symmetric group $S_{r}$. For $r = 6$, we show the number of exceptional $n le N$ for which the Galois group of this polynomial is not $S_r$ is at most $O(log N)$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
