A database of local fields

@article{Jones2006ADO,
  title={A database of local fields},
  author={John W. Jones and David P. Roberts},
  journal={J. Symb. Comput.},
  year={2006},
  volume={41},
  pages={80-97}
}

Figures and Tables from this paper

A database of number fields
We describe an online database of number fields which accompanies this paper. The database centers on complete lists of number fields with prescribed invariants. Our description here focuses on
High-Speed Calculation for Isomorphy of Extensions of a p-adic Field with Magma(Theory)
In this paper, we present an efficient algorithm for isomorphy of extensions of a p-adic field. Mainly, we deal with extensions of degree p.
Counting Tamely Ramified Extensions of Local Fields up to Isomorphism
TLDR
This paper gives a formula that counts the number of degree n tamely ramified extensions of K in the case p is of order 2 modulo n.
Octic 2-adic fields
Number Fields Ramified at One Prime
TLDR
The existence of G-p fields for fixed G and varying p is Westudy's conjecture.
Nonic 3-adic Fields
TLDR
All nonic extensions of Q3 are computed and it is found that there are 795 of them up to isomorphism and the associated Galois group of such a field is described.
On unit signatures and narrow class groups of odd abelian number fields: Galois structure and heuristics
  • Mathematics
  • 2021
This paper is an extension of the work of Dummit and Voight on modeling the 2-Selmer group of number fields. We extend their model to Sn-number fields of even degree and develop heuristics on the
An identification for Eisenstein polynomials over a p-adic field
In this note, we give a criteria whether given two Eisenstein polynomials over a padic field define the same extension (Proposition 1.6). In particular, we completely identify Eisenstein polynomials
Computing the Galois group of a polynomial over a p-adic field
TLDR
A family of algorithms for computing the Galois group of a polynomial defined over a p-adic field are presented, apart from the "naive" algorithm, the first general algorithms for this task.
Leopoldt-type theorems for non-abelian extensions of Q
. We prove new results concerning the additive Galois module structure of certain wildly ramified finite non-abelian extensions of Q . In particular, when K/ Q is a Galois extension with Galois group G
...
...

References

SHOWING 1-10 OF 39 REFERENCES
On the computation of all extensions of a p-adic field of a given degree
TLDR
An algorithm for the computation of generating polynomials for all extensions K/k of a given degree and discriminant for p-adic field k is presented.
Octic 2-adic fields
Nonic 3-adic Fields
TLDR
All nonic extensions of Q3 are computed and it is found that there are 795 of them up to isomorphism and the associated Galois group of such a field is described.
A_6-extensions of Q and the mod p cohomology of GL(3,Z)
We present six examples of 3-dimensional mod p Galois representations of type A_6 for which we were able to obtain computational evidence for the generalization of Serre's Conjecture proposed by Ash,
A database for field extensions of the rationals
TLDR
A database of field extensions of the rationals, its properties and the methods used to compute it is reported on, finding that current methods for the realization of groups as Galois groups have limitations if the signature of the resulting Galois extension is also prescribed.
SL3 (F2)-Extensions of Q and Arithmetic Cohomology Modulo 2
We generate extensions of Q with Galois group SL3(F2) giving rise to three-dimensional mod 2 Galois representations with sufficiently low level to allow the computational testing of a conjecture of
A6-extensions of Q and the modp cohomology of GL3(Z)☆
A Survey of Trace Forms of Algebraic Number Fields
Every finite separable field extension F/K carries a canonical inner product, given by trace(xy). This symmetric K-bilinear form is the trace form of F/K.When F is an algebraic number field and K is
Sextic Number Fields with Discriminant - j 2 a 3 b
Complete lists of number fields, of given degree n and unramified outside a given finite set S of primes, are both of intrinsic interest and useful in some applications. For degrees n ≤ 5 and S = {∞,
...
...