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 35416
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
45
votes
Accepted
Has Fermat's Last Theorem per se been used?
Corollary 3.17 in this paper of Stefan Keil uses FLT for exponent 7 to show that if $E/\mathbb{Q}$ is an elliptic curve with a rational 7-torsion point $P$, and $E\rightarrow E'$ is the 7-isogeny with …
- 13k
19
votes
Accepted
how to compute Hilbert class field of $\Bbb Q(\zeta_{23})$?
The cyclotomic field $K=\mathbb{Q}(\zeta_{23})$ contains the quadratic field $F=\mathbb{Q}(\sqrt{-23})$, and $F$ has class number $3$ (it is the first quadratic field, when those are ordered by absolu …
- 13k
19
votes
Accepted
How to picture $\mathbb{C}_p$?
You do whatever works for you. Some people think more algebraically, others more geometrically. I certainly don't know what "to picture" means in this context, but then, I am a more algebraic person, …
- 13k
17
votes
Accepted
Order of Ш (Sha)
No, there are no such examples known. In fact, with the current technology, the two questions are more or less equally hard. That's because for any given prime $p$, you can, in principle, establish fi …
- 13k
17
votes
0
answers
1k
views
Special values of Artin L-functions
This question might be naive and might carry the heuristic that we are living in the best possible world a little too far. If so, I appreciate being told so.
Background: Stark's conjecture interprets …
- 13k
16
votes
Accepted
Regulators of Number fields and Elliptic Curves
Let me first give you a heuristic "reason", why the regulator in the class number formula looks different from the regulator in the Birch and Swinnerton-Dyer conjecture. It is often more convenient (a …
- 13k
16
votes
Accepted
Is there any conditions on a finite abelian group so that it cannot be class group of any nu...
It follows from the Cohen-Lenstra heuristic that every finite abelian group is expected to be isomorphic to infinitely many class groups of real quadratic fields (even to a positive proportion of real …
- 13k
14
votes
Heuristics of Cohen-Lenstra-Martinet
The answer to the question as stated is "no". The original Cohen—Lenstra—Martinet heuristics say nothing about the $2$-Sylow subgroup of the class group of a quadratic field.
These heuristics were lat …
- 13k
14
votes
Accepted
Finite order elements of $\mathrm{GL}_d(\mathbb{Z})$ that are conjugate to powers of themselves
The answer is "no" in general. There may be an elementary way of seeing this, but I will frame this in representation theoretic terms and will describe a general construction.
The question is equivale …
- 13k
14
votes
2
answers
1k
views
Class groups in dihedral extensions - some sort of Spiegelungssatz?
Let $p$ be an odd prime and let $F/\mathbb{Q}$ be a Galois extension with Galois group $D_{2p}$, let $K$ be the intermediate quadratic extension of $\mathbb{Q}$, and $L$ an intermediate degree $p$ ext …
- 13k
13
votes
Fermat's last theorem over larger fields
There might well be an elementary construction of infinitely many points (which I cannot think of right now), but in any case, I think that there are experts out there who expect there to be infinitel …
- 13k
12
votes
On a minimal algebraic number field which satisfies the principal ideal theorem
The answer to your first question is "no". In general, if $K/k$ is a cyclic unramified Galois extension of odd order, then the order of the capitulation kernel (the subgroup of the class group of $k$ …
- 13k
12
votes
An explicit computation in class field theory
In your particular case, $K^{ab}$ is completely understood, but your field is one of the very few for which such an explicit class field theory is known, so you got lucky.
I don't know your backgroun …
- 13k
10
votes
How to compute Hilbert class field of $\Bbb Q(\zeta_{31})$?
This is a fun question, and I had already been thinking of making some comments on this in the question you link to. Apologies in advance for the long post.
Actually, the quadratic subfield of $\mathb …
- 13k
8
votes
Accepted
What is the ring $A_{\Gamma}$ in the Cohen-Lenstra Heuristics?
The group $\Gamma$ is indeed isomorphic to the Galois groups of the fields in the family, whose class groups one studies. The class groups come with a natural action of $\Gamma$, but under this action …
- 13k