Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with algebraic-number-theory
Search options not deleted
user 18238
Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces
4
votes
Accepted
Generalization of Hilbert 94 and capitulation
The answer to both my question is that "adding conductors does not change anything". Olivier has already discussed this for the Principal Ideal Theorem, and for Hilbert 94 this is proven by Suzuki in
…
- 5,670
8
votes
1
answer
1k
views
Generalization of Hilbert 94 and capitulation
Let $L/K$ be a finite, cyclic extension of number fields, say with $\mathrm{Gal}(L/K)=G$. In my context $G$ is actually of order $p$, an odd prime number, but let me state my question for every cyclic …
- 5,670
1
vote
Accepted
What are conditions to satisfied by rational prime p so that every prime lying above p is a ...
First of all, as they observe, the assumption that $H(K)/\mathbb{Q}$ is abelian ensures that $H(K)\subseteq\mathbb{Q}(\zeta_{f(K)})$ and not only $K\subseteq\mathbb{Q}(\zeta_{f(K)})$. Also, they work …
- 5,670
2
votes
Accepted
The kernel of the global class field theory homomorphism
Well, actually the kernel of $\theta$ is perfectly explicit and it is the connected component of the identity in $C_K$: see, for instance, Artin-Tate Class Field Theory, Chapter IX, §1. Theorem 3 ibid …
- 5,670
6
votes
Ideal classes fixed by the Galois group
As Franz Lemmermeyer suggested, one should consider the so-called Ambigous Class Number Formula: you find it, for instance, in Gras' book "Class Field Theory", II.6.2.3.
It says that if $L/K$ is a fi …
- 5,670
5
votes
0
answers
270
views
Why does the longitude correspond to Frobenius in Arithmetic Topology, and other strange phe...
I am trying to adress Morishita's book Knots and Primes to discover a bit about Arithmetic Topology, but some analogies puzzle me. I know that the correspondence should be addressed with a grain of sa …
- 63.9k
0
votes
Accepted
About real abelian number fields
Let $J^{(p)}\subseteq J$ be the subfield fixed by the $p$-Sylow subgroup of $\operatorname{Gal}(J/K)$ which is also the $p$-Sylow subgroup of the (abelian!) group $\operatorname{Gal}(J/\mathbb{Q})$ si …
- 5,670
1
vote
references on group representation over local fields / a question on an argument of a Ralph ...
Your question has nothing to do with $p$-adic representations, it is a general fact about representations of finite groups. Given a group $\Delta$ and a field $F$ of characteristic $0$ (characteristic …
- 5,670
2
votes
Accepted
Rationality of trace of endomorphism of Iwasawa-thing
This is not really an answer, just a (very!) long comment. Everything I write is obvious for people working in Iwasawa theory, and I apologize for the trivialities.
Let me start by your final paragra …
- 5,670
2
votes
Computing the relative class group (with Galois action) of relatively large cyclotomic groups
Have you had a look at Schoof's paper The structure of the minus class group of abelian number fields, Séminaire de Théorie des Nombres de Paris, 1988--89? Schoof's idea is to conjecture that the Fitt …
- 5,670
1
vote
Accepted
Kummer congruences for totally real number fields
I think that the point lies in the difference between a primitive and imprimitive $L$-function. Before entering the details, let me observe that Washington's definition of $p$-adic $L$-functions (as t …
- 5,670
4
votes
Accepted
Class groups in dihedral extensions - some sort of Spiegelungssatz?
I normally don't like to cite my own work on MO, but this time the preprint arXiv:1803.04064 was written, together with L. Caputo, having the OP's question in mind; and so, first of all, let me thank …
- 5,670
5
votes
Accepted
Refinement of (classical) Iwasawa main conjecture
There is an answer which follows from Kolyvagin's theory of Euler Systems, and can be found in Theorem 4.4 of
K. Rubin, Kolyvagin's System of Gauss Sums, in Arithmetic Algebraic Geometry, van der Gee …
- 5,670
6
votes
Accepted
The $\ell$- part of the class groups of the $p$-cyclotomic fields
As Keith Conrad observed in his comment, what you are asking about is Washington's theorem which is either in his book, referenced as Theorem 16.12, or in his original paper in Invent. Math. He proved …
- 37k
6
votes
An elementary, short proof that the group of units of the ring of integers of a number field...
I do not know if the following qualifies as "short" or "elementary": but it does not follow the usual pattern through Minkowski's Convex Body Theorem. Rather, it mimics the classical proof of Mordell– …
- 5,670