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Results tagged with nt.number-theory
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user 69196
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
4
votes
2
answers
534
views
A galois group is topologically finitely generated or finitely generated as a $\mathbb{Z}_p$...
The basic set up is the following:
Let $K$ be a number field. let $p$ be an odd prime. Let $\Sigma_p$ be the set of primes of $K$ lying above $p$. Let $M$ be the composite of all finite $p$-extensions …
- 313
2
votes
0
answers
537
views
Fontaine - Wintenberger field of norms and imperfect case
Let $K$ be a complete discrete valued field whose residue field $k_K$ has characteristic $p$ and has the property that $[k_K:k_K^p]=p^d$ for some $d$. Let $t_{\alpha}, 1 \leq \alpha \leq d$ be a set o …
- 313
3
votes
0
answers
152
views
Finiteness of points over the cyclotomic extension for modular forms
Let $\rho(f):G_\mathbb{Q} \rightarrow GL_2(K_f)$ be the Galois representation attached to some cuspidal modular form $f$ where $K_f$ is a finite extension of $\mathbb{Q}_p$.
Let $V_f$ be the vector s …
- 313