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Jan
28
comment Proofs of Fermat-Wiles theorem for exponent 3
While we are at it. It seems the question is equivalent to finding that the rank of the elliptic curve 27a3 is zero over $\mathbb{Q}$ as it is easy to find its torsion points. So for instance computing the modular symbol $[0]=1/9\neq0$ tells us that the $L$-series does not vanish at $s=1$ and hence by Gross-Zagier-Kolyvagin, we know that the rank is 0. Or by a theorem of Kato, too.
Jan
11
comment If $K=\langle$HCF of $\mathbb{Q}_{p}$, $\mathbb{Q}^\mathrm{cycl}\rangle$, does $K$ also contain all roots of elements of $\mathcal{O}_{K}^{\times}$?
An example of a bad edit in my opinion. The HCF in the title is not clear. Local fields don't have Hilbert class fields, global fields have them. The version before wasn't good, but better.
Jan
11
reviewed Reject If $K=\langle$HCF of $\mathbb{Q}_{p}$, $\mathbb{Q}^\mathrm{cycl}\rangle$, does $K$ also contain all roots of elements of $\mathcal{O}_{K}^{\times}$?
Jan
11
comment Lifting a real quadratic twist of an Elliptic Curve to the modular curve
Your second curve $E_{\sqrt{p}}$, am I right assuming it is the curve defined over $\mathbb{Q}$ obtained by twisting $E$ by $p$ ? If so the conductor of it is $p^2N$ in most cases, unless $p$ divided $N$ and you are lucky.
Dec
27
comment Points $\alpha_n$ of $A$ over the $m_n$-th layer in a $\mathbb{Z}_p$-ext. of $K$, where $A$ is an Ab. var. and $m_n$ is strictly increasing
Are you assuming that $A(K_{p^n})$ are all finitely generated? Otherwise you could just have $A(L)=A(K_{p^1})$ and the answer is "no".
Dec
26
comment Is there $t\in\operatorname{Gal}(\overline{K}/K)$ s.t. $\operatorname{rank}_{\mathbf{Z}_p}((t-1)E_{p^\infty}(\overline{K}))=1$?
Some suggestions for corrections: $K$ should be the compositum of these fields not the union. Either the dimension is a corank or it is the rank, but the $p$-primary part is replaced by the Tate module.
Dec
25
reviewed Approve Can we find an upper bound?
Dec
24
reviewed Approve Is there a limit of $\cos (n!)$?
Dec
3
comment Ranks of elliptic curves over Q(t)
Oh, sorry that should be "Section III.2".
Dec
3
comment Ranks of elliptic curves over Q(t)
Section II.2 in Silverman's "Advanced topics in the arithmetic of elliptic curves"
Nov
13
awarded  Custodian
Nov
13
reviewed Approve Irrationality of $ \pi e, \pi^{\pi}$ and $e^{\pi^2}$
Nov
9
awarded  Nice Answer
Nov
9
revised Galois cohomologies of an elliptic curve
added 15 characters in body
Nov
9
comment Galois cohomologies of an elliptic curve
That is why I took $m$ odd. Oh, but I forgot that in the local case. I correct that now. Thanks.
Nov
8
answered Galois cohomologies of an elliptic curve
Oct
8
reviewed Approve A family of convex bodies in Banach-Mazur position
Oct
7
comment What is the fastest algorithm for counting points in elliptic curves mod n?
Sort of converse to Felipe's answer: If the factorisation of $n$ is known then it suffices to find the number of points on the curve modulo the prime factors.
Sep
17
comment Serre's surjective theorem importance
Equivalently: The Galois group of $K(E[\ell])$ is isomorphic to $\operatorname{GL}_2(\mathbb{F}_{\ell})$. This field turns up when one does an $\ell$-descent, or more generally when one studies the $\ell$-Selmer group. For instance for an Euler system it is great to have a large Galois group there, for an explicit $\ell$-descent it is rather the opposite.
Sep
8
comment The Birch-Swinerton-Dyer conjecture for rank 1
The list of books and articles to give as reference to cover all these topics would be rather long - and it will depend on the level of how much you already understand. Maybe the list at math.harvard.edu/~yihang/GZSeminar.html will help.