Symplectic Groups as Galois Groups
β Scribed by Nicholas F.J. Inglis
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 66 KB
- Volume
- 227
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We give an algorithm for the determination of the finitely many primes such that the image of the modular Galois representations attached to a weight 2 newform on Ξ 0 (N ) without complex multiplication or inner twists may not be "as large as possible". We apply the algorithm to suitable newforms a
The construction starts with a polynomial with Galois group the given group and is based on representation theory.
In this paper, we consider nonsplit Galois theoretical embedding problems with cyclic kernel of prime order p, in the case where the ground field has characteristic / p. It is shown that such an embedding problem can always be reduced to another embedding problem, in which the ground field contains
Galois groups of irreducible trinomials X n + aX s + b β X are investigated assuming the classification of finite simple groups. We show that under some simple yet general hypotheses bearing on the integers n s a and b only very specific groups can occur. For instance, if the two integers nb and as
For any integer n 7, we show how to explicitly build an infinite number of rational trinomals of degree n whose Galois group over Q is isomorphic to A n .