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Results tagged with nt.number-theory
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user 117693
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
4
votes
0
answers
163
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What are the applications of $\lambda$-rings to class field theory?
In the book Lambda Rings by Yau, he mentions several areas where $\lambda$-rings can be applied, but he doesn't go into much details. He even includes class field theory in the list, mentioning "finit …
- 804
12
votes
1
answer
641
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What kind of arithmetic information does the ring of integers in an infinite extension carry?
The fact that the ring of integers in a finite extension of $\Bbb Q$ is a Dedekind domain and purely algebraic properties of Dedekind domains are absolutely essential for algebraic number theory. So i …
- 804
2
votes
0
answers
263
views
Is there any relation between Berkovich spaces over $\Bbb Z$ and Arakelov theory?
As I understand it, both Arakelov geometry and Berkovich geometry over $\Bbb Z$ (or $\mathcal O_K$) consider geometric objects that contain in some sense information about both archimdean and nonarchi …
- 804
7
votes
1
answer
351
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Shouldn't we expect analytic (in the Berkovich sense) étale cohomology of a number field to ...
Let $K$ be a number field. Consider $X=\mathcal{M}(\mathcal O_K)$ the global Berkovich analytic space associated to $\mathcal O_K$ endowed with the norm $\|\cdot\|=\max\limits_{\sigma:K \hookrightarro …
- 804