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A database of number fields
- Mathematics
- 2014
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)
- Mathematics
- 2012
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
- MathematicsIntegers
- 2016
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.
Number Fields Ramified at One Prime
- MathematicsANTS
- 2008
The existence of G-p fields for fixed G and varying p is Westudy's conjecture.
Nonic 3-adic Fields
- MathematicsANTS
- 2004
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
- Mathematics
- 2011
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
- Mathematics, Computer Science
- 2020
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
- Mathematics
- 2021
. 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…
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Nonic 3-adic Fields
- MathematicsANTS
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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)
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