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 14835
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
20
votes
1
answer
1k
views
What was a "cusp" to Hurwitz in 1892?
Let $d\in\mathbb{N}$
be squarefree.
Let $\mathcal{O}_d$
be the ring of integers of $\mathbb{Q}(\sqrt{-d})$.
Let $\Gamma_d=\mathrm{PSL}_2(\mathcal{O}_d)$.
Let $\mathcal{H}^3$
be the upper half-space mo …
- 2,436
2
votes
Accepted
Some general properties of arithmetic groups of simplest type
The book Conformal Geometry of Discrete Groups and Manifolds by Boris N. Apanasov contains a detailed description of what it means for a group to be arithmetic, and why the definition manifests as it …
- 5,259
2
votes
2
answers
479
views
Some general properties of arithmetic groups of simplest type
I'm working in the area of arithmetic Kleinian groups (as discrete groups of motions of hyperbolic 3-space). For the more general case of hyperbolic $n$-space, there is a particular class of arithmet …
- 5,259
6
votes
1
answer
231
views
Current interest in geometric properties of Hilbert fundamental domains
Harvey Cohn published several articles in the 1960's analyzing geometric properties of fundamental domains for Hilbert modular surfaces.
H. Cohn, "On the shape of the fundamental domain of the Hilbe …
- 2,436
5
votes
0
answers
208
views
Dirichlet domain for a Hilbert modular variety
There is existing literature on fundamental domains for Hilbert-Blumenthal surfaces, perhaps most noticeably what Siegel did. I am interested in whether such fundamental domains have been approached u …
- 2,436
6
votes
3
answers
625
views
For an arithmetic hyperbolic 3-manifold group, when is its trace field not its invariant tra...
Edit: In my original post I failed to require the group to be a manifold group. The answer below from @BenLinowitz works in that case. I am really interested though in when the group is torsion-free, …
- 2,436
2
votes
1
answer
306
views
What is the effect of imaginary quadratic extension on a quaternion algebra's ramified primes
A smart man once explained to me how to solve the following problem, then I forgot.
Let $F\subset\mathbb{R}$
be a number field,
let $d\in F^+$,
and let $K=F(\sqrt{-d})$.
Denote the rings of integers …
- 2,436
6
votes
1
answer
387
views
Computing algebraic properties of trace fields, as given by SnapPy
SnapPy can tell you the trace field of a hyperbolic $3$-manifold (which is awesome), but it specifies the field by outputting:
the minimal polynomial of the field over $\mathbb{Q}$, and
a decimal ap …
CommunityBot
- 1
6
votes
1
answer
341
views
Compact hyperbolic 3-manifolds with prescribed quaternion algebra, quaternion parameters as ...
What is an interesting class of examples of hyperbolic 3-manifolds,
each of which satisfies the following conditions?
1. It is compact
2. Its trace field contains a unique imaginary quadratic extens …
CommunityBot
- 1
2
votes
1
answer
240
views
Why do noncocompact arithmetic Kleinian groups have quadratic trace fields?
I realize there are a few different ways of going about proving this, depending on one's background, but there's a particular number theoretic aspect that I am just blanking on, and can't seem to find …
- 2,436
13
votes
3
answers
496
views
Origin of number theoretic invariants associated to hyperbolic 3-manifolds
I've been studying number theoretic methods of classifying hyperbolic 3-manifolds for over a year now. In particular, there is are the trace field, invariant trace field, quaternion algebra, and inva …
- 68.8k
2
votes
1
answer
197
views
Frohman & Fine's proof about Bianchi groups as HNN extensions (or anyone else's)
Specifically, I am looking for a proof that for squarefree $d\in\mathbb{N}\setminus\{ 1,3\}$, there exists some Kleinian $\Gamma$ and some $\alpha\in$Aut$(PSL(2,\mathbb{Z}))$, such that the Bianchi gr …
- 2,436
0
votes
Accepted
Frohman & Fine's proof about Bianchi groups as HNN extensions (or anyone else's)
The second reference listed in the question,
Charles Frohman and Benjamin Fine, "Some Amalgam Structures for Bianchi Groups," 1988, Proceedings of the American Mathematical Society, Vol. 102, No. 2, …
- 2,436
1
vote
1
answer
248
views
Definition of level N congruence subgroup of an arithmetic group, useful for computations
My title requests something more general than I actually require right now, so I would settle for an answer to something more specific (details below) but I would like to understand the more general c …
- 2,436
0
votes
Accepted
Definition of level N congruence subgroup of an arithmetic group, useful for computations
Thank you to @Qiaochu Yuan and @Alex B. for the kick in the right direction. Here is the answer to this question for the case introduced in the third paragraph. Hopefully it benefits someone other t …
- 2,436