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Results tagged with nt.number-theory
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user 1729
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
16
votes
Accepted
Tamely ramified p-adic Galois representations
It's true that if $\rho$ is tamely ramified, then $\rho$ is de Rham. In fact, it's even potentially crystalline with all Hodge-Tate weights equal to 0.
First, note that $\rho(I_{\mathbb Q_p})$ is fin …
- 1,388
24
votes
In which ways can the isogeny theorem fail for local fields?
I think the statement can fail in the case of elliptic curves of good reduction even when $l = p$. But then your comment on
Serre-Tate theory confused me for a little while! (A discussion with Jared W …
- 1,388
16
votes
Accepted
Geometric vs Arithmetic Frobenius
Geometric and arithmetic Frobenius live in a Galois group, they are different from the Frobenius morphism. The Galois group of a finite field of cardinality $q$ has a canonical generator $x \mapsto x^ …
3
votes
Rational congruence of binomial coefficient matrices
There is a problem with this approach (I refer to Wadim Zudilin's answer). At least I don't see how to get from the first displayed equation (involving the $P_i$) to the second (involving the $L_i$) i …
- 1,388