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 144623
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
1
vote
1
answer
269
views
$K_v(a^{1/m}) /K_v$ is unramified if only if $v(a)≡0 \pmod m$
Let $K$ be a number field and $v$ be it's one of $K$'s non-archimedian valuation.
Then, I would like to prove $K_v(a^{1/m}) /K_v$ is unramified if
only if $v(a)≡0 \pmod m$.
This is from Silverman' …
- 1,531
0
votes
0
answers
141
views
Why is image of prime ideal under Hecke (Grossencharacter) character is prime element of the...
Let $K$ be a imaginary quadratic field, and $E/K$ be elliptic curve which has CM over $K$.
Let $ψ_E$ be Hecke(Grossencharacter) character of $E/K$.
Let fix prime ideal $I$ of $K$.
Then, why $ψ_E(I)$ …
- 1,531
1
vote
0
answers
111
views
Rayclass group and Hilbert class group, $\mathrm{Gal}(K(\mathfrak{a})/K)\cong(\mathcal{O}_K/...
Let $K$ be an imaginary quadratic field with class number $1$. Let $\mathfrak{a}$ be an ideal of $ \mathcal{O}_K$ and $K(\mathfrak{a})$ denote the ray class field of $K$ modulo $\mathfrak{a}$.
Why doe …
- 1,531
0
votes
0
answers
121
views
Rank growth of elliptic curve $E:y^2=x^3-17$ in quadratic number field
Let $E:y^2=x^3-17$ be an elliptic curve.
It is known that rank$(E/\Bbb{Q})=0$.
(For example, prop $6.5$, $362$p in Silverman's book 'The arithmetic of elliptic curves')
Over $K=\Bbb{Q}(i)$, what is t …
- 1,531
1
vote
0
answers
127
views
How Galois group acts on Tate-Shafarevich group?
Let $L/K$ be a quadratic number field extension. Let $\operatorname{Sha}(E/L)$ be Tate-Shafarevich group of elliptic curve $E/L$.
How $\sigma \in \operatorname{Gal}(L/K)$ acts on $\operatorname{Sha}(E …
- 1,531
4
votes
1
answer
267
views
Order of $37$-Sylow subgroup of ideal class group of $K_{37} = \Bbb Q(\mu_{37^{n}})$ is know...
I want to examine nontrivial examples of what we call Iwasawa class formula,
$c(n)=\mu p^n + \lambda n + \nu$, where $\lambda, \mu \in \mathbf N$ and $\nu \in \mathbf Z$ are parameters depending only …
- 1,531
0
votes
0
answers
77
views
Local field such that the value group of $K^\text{perf}$ ( perfect closure of $K$) is $\bigc...
Let $K$ be a local field of positive characteristic.
I'm looking for a $K$ which satisfies the following condition.
Value group of $K^\text{perf}$ (perfect closure of $K$) is $\bigcup_{n\geqq1}(1/p^n …
- 1,531
3
votes
1
answer
382
views
Completion of infinite degree extension of perfectoid fields is perfectoid?
Is completion of infinite degree extension of perfectoid fields perfectoid ?
It is known that finite extension of perfectoid fields is also perftoid from tilting correspondence, but what about infinit …
- 1,531
0
votes
0
answers
122
views
How extension $\Bbb{Q}_p(\hat{E}[p])/\Bbb{Q}_p$ looks like?
Let $E/ \Bbb{Q}_p$ be an elliptic curve over $ \Bbb{Q}_p$. $\hat{E}$ denote the corresponding formal group of $E$.
I want to know what
$\Bbb{Q}_p(\hat{E}[p])/\Bbb{Q}_p$ is .
At first I tried to prove …
- 1,531
3
votes
0
answers
109
views
Local global principle over infinite extension of $\Bbb{Q}$ which is not algebraically closed
Let $A$ be an algebraic variety over a field $K$, which is finite extension of $ \Bbb{Q}$.
We say local global principle holds if $A(K_v) \neq \emptyset$ implies $A(K) \neq \emptyset$, where $K_v$ is …
- 1,531
3
votes
0
answers
126
views
Isogeny of elliptic curve over positive characteristic $p$ which does not come from characte...
Let $K$ be quadratic imaginary field. Let $E$ be an elliptic curve which has CM over $R_K$
($R_K$ is ring of integers of $K$).
According to SIlverman's ''ADvanced topics in the arithmetic of elliptic …
- 1,531
1
vote
0
answers
133
views
Characterization of Selmer group in terms of two descent
This question is about p 337 of Silverman's book ''The arithmetic of elliptic curves'', p 337, http://www.pdmi.ras.ru/~lowdimma/BSD/Silverman-Arithmetic_of_EC.pdf.
Let $E:y^2=x^3+ax^2+bx$ and $E':Y^2= …
- 1,531
2
votes
0
answers
186
views
Relation between division point of elliptic curve and formal group of elliptic curve, $\Bbb{...
Let $E/ \Bbb{Q}_p$ be an elliptic curve over $ \Bbb{Q}_p$. $\hat{E}$ denote the corresponding formal group of $E$.
I want to prove
$\Bbb{Q}_p(E[p])＝\Bbb{Q}_p(\hat{E}[p])$.
$ \hat{E}[p]$ denotes $p$ di …
- 1,531
0
votes
0
answers
133
views
Proof of $[p](x)≡x^p\operatorname{mod}p \Bbb{Z}_p$ for formal group of elliptic curve
Let $E$ be an elliptic curve over $\Bbb{Q}_p$.
Let $ \hat{E}$ be formal group of $E$.
Let $[p](x)＝x＋_\hat{E}＋・・・＋_\hat{E}x$ (add by formal group law $p$ times).
I want to know the proof of $[p](x)≡x^ …
- 1,531
2
votes
1
answer
222
views
Can the number of elements of order 4 in the Tate–Shafarevich group grow arbitrarily large?
Let $E/K$ be a number field. For quadratic field extensions $L/K$, it is known that $\operatorname{Ш}(E/L)[2]$ can be arbitrarily large (cf. P. L. Clark and S. Sharif, "Period, index and potential Sha …
- 1,531