All Questions
Tagged with class-field-theory arithmetic-geometry
8 questions with no upvoted or accepted answers
11
votes
0
answers
381
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What are the possible bad reductions for an abelian variety of dimension $g$ and a maximal endomorphism ring?
Perhaps the most basic fact about abelian varieties with CM is they have an everywhere potential good reduction (Serre-Tate). On the face of it it might appear that there isn't much more to be added ...
- 13.8k
3
votes
0
answers
215
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Global class field theory and closure of unit groups
I'm looking for a reference for the following facts from global class field theory that I found without proofs. I will state them as questions, just in case I get the statement wrong. We fix $K$ a ...
- 85
2
votes
0
answers
250
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Maximal p-extension and pro-p extension
I’m studying Iwasawa theory and I meet some questions Thanks a lot for your help.
Q_1: About terminology $p$-extension.
I find many reference use maximal $p$-extension or maximal abelian p-extension ...
- 319
2
votes
0
answers
128
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How do elliptic units generate the module of Euler systems over abelian extensions of imaginary quadratic fields?
I am trying to undesrtand the analogy between the Euler systems over abelian extensions of the rationals and the Euler systems over abelian extensions of imaginary quadratic fields.
As Soogil Seo ...
- 99
2
votes
0
answers
254
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Global sections of higher direct images
If $f : X\to V$ is a smooth proper map of smooth schemes, what are the global sections of
$R^if_{fppf, *}\mu_p$
$R^if_{fppf, *}\mathbb{G}_{\rm m}$
I was reading Milne's book "Arithmetic duality", ...
user113393
1
vote
0
answers
210
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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
1
vote
0
answers
180
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Maximal unramified extension and algebraic closure of $\operatorname{Frac}(\widehat{A_{\mathfrak{m}_A}})$
$\DeclareMathOperator\trdeg{trdeg} \DeclareMathOperator\Frac{Frac} $
Let $k$ be an algebraically closed field of characteristic $0$ and $K$ a function field over $k$. let $(A, \mathfrak{m}_A)$ a ...
- 5,966
1
vote
0
answers
54
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Finite generation for a restricted ramification idele module
Let $k$ be a number field, let $\bar k \subseteq \mathbb{C}$ be a fixed algebraic closure of $k$, and let $S$ be the set of infinite primes of $k$. Denote by $k_S$ the maximal extension of $k$ inside $...
- 11.3k