[過去ﾛｸﾞ] 現代数学の系譜 工学物理雑談 古典ガロア理論も読む78 (1002ﾚｽ)
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308(1): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE 2019/10/29(火)14:42 ID:wEoW+rwB(5/9) AAS
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「Inverse Galois problem group PSL(2,16):2 of degree 17」
約 64 件 （0.70 秒）
下記以外にも面白そうなのがあるが
下記は、”Ihara/Ribet/Serre (eds.)”と”Noriko Yui”が目にとまったので
PDF This book describes a constructive approach to the inverse ...
library.msri.org ? books ? Book45 ? files ? book45
15. Hochster/Huneke/Sally (eds.): Commutative Algebra. 16. Ihara/Ribet/Serre (eds.): Galois Groups over q. 17 ... 17. 1.2. Resolvent Polynomials. 23. Exercises. 26. Chapter 2. Groups of Small Degree. 29. 2.1. Groups of Degree 3. 30. 2.2. Groups ....
The classical Inverse Problem of Galois Theory is the existence problem for ...... PSL2(Fq): the projective special linear group of 2 × ...
Mathematical Sciences Research Institute
Publications
45 Generic Polynomials Constructive Aspects of the Inverse Galois Problem
Mathematical Sciences Research Institute 2002
Christian U. Jensen
University of Copenhagen
Arne Ledet
Texas Tech University
Noriko Yui
Queen’s University, Kingston, Ontario
P4/268
Mathematical Sciences Research Institute Publications
16 Ihara/Ribet/Serre (eds.): Galois Groups over
P16
Methods of Ihara, Schneps, etc. There is an excellent MSRI Conference
Proceedings Galois Groups over Q, [IR&S], edited by Ihara, Ribet and Serre.
There the absolute Galois groups acting on algebraic fundamental groups were
extensively discussed.
P249
[IR&S] Y. Ihara, K. Ribet & J.-P. Serre (eds.), Galois Groups over
, Mathematical Sciences
Research Institute Publications 16, Springer-Verlag, 1987
318(1): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE 2019/10/30(水)17:11 ID:xePUfid4(1/5) AAS
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下記
”generic polynomials”
”Theorem 0.5.1. (Brumer) A generic polynomial for the dihedral group D5
of degree 5 over an arbitrary field K is given as follows:
f(s, t,X) = X^5 + (t ? 3)X^4 + (s ? t + 3)X^3 + (t2 ? t ? 2s ? 1)X^2 + sX + t
over K(s, t) where s and t are indeterminates.”
は、興味深いね
外部ﾘﾝｸ[pdf]:library.msri.org
Mathematical Sciences Research Institute
Publications 45
Generic Polynomials
Constructive Aspects of the Inverse Galois Problem
Christian U. Jensen
University of Copenhagen
Arne Ledet
Texas Tech University
Noriko Yui
Queen’s University, Kingston, Ontario
university of cambridge
Mathematical Sciences Research Institute 2002
(抜粋)
0.5. Description of Each Chapter ・・・P9
We also exhibit generic polynomials for the groups of degree 3, 4 and 5. For instance, we
have the following result:
Theorem 0.5.1. (Brumer) A generic polynomial for the dihedral group D5
of degree 5 over an arbitrary field K is given as follows:
f(s, t,X) = X^5 + (t ? 3)X^4 + (s ? t + 3)X^3 + (t2 ? t ? 2s ? 1)X^2 + sX + t
over K(s, t) where s and t are indeterminates.
We also demonstrate the non-existence of a generic C8-polynomial over Q,
and as a consequence get the following two examples of fixed subfields of the
function field Q(s, t, u) in three indeterminates s, t, u, both with a C4-action,
where one is rational and the other not:
Theorem 0.5.2. (a) Let be the automorphism on Q(s, t, u) given by
略
(引用終り)
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