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Results tagged with nt.number-theory
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user 105625
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
12
votes
1
answer
468
views
Finite Galois module whose Ш¹ is nonzero?
In algebraic number theory, we constantly make use of the nine-term Poitou-Tate sequence: Let $K$ be a number field and $M$ a finite $K$-Galois module. Then we have the nine-term exact sequence
$$
H^0 …
- 636
4
votes
Accepted
Is an integral sum of periodic vectors always a sum of integral periodic vectors?
A beautiful question! Though I don't have the time or the space to fill in all the details, I think one can answer the question in the following way. The answer is yes.
We can reformulate the questio …
- 636
2
votes
Accepted
Artin map restricted to base field
I've finally found the answer to my question by perusing Serre's Local Fields, Ch.XIII, specifically Propositions 10-12, which contain the functorial properties of the Artin symbol used below.
We des …
- 636
5
votes
1
answer
421
views
Artin map restricted to base field
Let $M/L/K$ be a tower of local fields such that $M/L$ is abelian with Galois group $G$. The Artin map $\psi_{M/L}$ restricted to $K^\times$ is a continuous map to $G$ and thus corresponds to some abe …
- 636