All Questions
9 questions
12
votes
1
answer
565
views
Parametrizing all cyclic extensions of the rational numbers of degree 5
Is there a polynomial $f(T,X) \in \mathbb{Q}(T)[X]$ in the indeterminate $X$ over the field $\mathbb{Q}(T)$ with $\mathrm{Gal}(f/\mathbb{Q}(T)) \cong \mathbb{Z}/5\mathbb{Z}$ such that for every Galois ...
- 11.3k
10
votes
0
answers
758
views
How does one understand geometric CFT in terms of modularity?
I have recently asked a question in a similar vein:
What makes Geometric CFT easier than CFT?
but I'm afraid I wasn't quite ripe to ask it yet. I have since consulted with the following sources:
http:/...
- 5,929
6
votes
1
answer
544
views
Chebotarev density theorem and pure weight local systems
How do we deduce the following statement from the Chebotarev density theorem? The statement is from Ngo's Fundamental Lemma paper.
Let $U$ be a scheme of finite type over $\mathbb{F}_q$. Let $\...
- 677
5
votes
1
answer
516
views
Reference for Local class field theory via witt vectors
I would like to find some books or lecture notes on geometric local class field theory via Witt vectors. I can't find any good paper on this subject.All approaches in the books to local class field ...
- 71
5
votes
0
answers
206
views
Real field of definition of an abelian variety of CM-type?
Question 0. Can a field of definitions (without automorphisms) of an (almost arbitrary) abelian variety of CM-type, originally defined over ${\mathbb{C}}$,
be chosen to be a totally real number ...
- 14.2k
3
votes
1
answer
326
views
Connected-étale sequence for ordinary CM elliptic curves
Let $E/k$ be an elliptic curve over algebraically closed field of characteristic $p$ with CM, for simplicity, by the maximal order of a quadratic imaginary field $K/\mathbb{Q}$.
Suppose that $p$ is ...
- 845
2
votes
0
answers
100
views
Quasi-algebraically closed fields reference request
I am looking for a road to understanding what quasi-algebraically closed fields are with the ultimate goal of understanding the paper by Lang 1952.
My current background is the first 6 chapters from ...
- 87
2
votes
0
answers
87
views
Rank growth in ray class fields of primes that are inert in an imaginary quadratic extension
If $K=\mathbb{Q}[\sqrt{-d}]$, $E$ is an elliptic curve and $\operatorname{rank}(E(K))=\operatorname{rank}(E(\mathbb{Q}))$, are there infinitely many primes $l$ of $\mathbb{Q}$ so that:
(1.) $\...
- 1,805
1
vote
0
answers
210
views
What is a definition of $A(P_v)$ in the definition of Brauer-Manin obstruction?
This is a question related to the definition of Brauer-Manin obstruction.
Let $K$ be a number field. $X/K$ be an algebraic variety over $K$.
Let $O_{X,P}$ be a local ring of $X$ at $P$. Let $Br(X)=\...
- 1,541