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 Yearling
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comment For $P$ $\mathbb{Z}G$-projective, $\mathbb{Q}\otimes P$ is $\mathbb{Q}G$-free
It is also exercise 16.4 in Serre's "Linear representations of finite groups".
Mar
30
awarded  Yearling
Mar
22
comment Elliptic curve : determine size of group $E/E_0$
Use Tate's algorithm. It is explained in Silverman 2 ("Advanced ...") or use Sage or Pari-GP or Magma to calculate the Tamagawa number. For your curve, also known as 102a1, it is $c_2 = 2$. (This is assuming you are interested in $E(\mathbb{Q}_2)/E^0(\mathbb{Q}_2)$ which may be different from the number of $\overline{\mathbb{Q}_2}$-points in the scheme $E/E^0$.)
Mar
17
comment Finiteness of the $p$-primary subgroup of an elliptic curve over the cyclotomic $\mathbb{Z}_p$-extension
Yes, they don't assume anything on $E$. It has more to do with the shape of the image of the global Galois representation on $T_pE$ rather than how this looks locally at $p$. In particular their proof splits up according to whether $E$ has cm or not.
Mar
17
answered Finiteness of the $p$-primary subgroup of an elliptic curve over the cyclotomic $\mathbb{Z}_p$-extension
Mar
15
comment Cohomology of elliptic curves
Indeed, André. It could be said that the question lacks the description of the background and the reason why the question is interesting. With further detail it will become clear if the question was intended as written currently or if there is a confusion as suggested by user84144. But I would think that the question is ok and should not be closed.
Mar
15
answered Cohomology of elliptic curves
Mar
9
comment Have locally principal crossed homomorphisms been studied?
One reference : Cohomology of number fields, a version of yoru kernel is denoted by $Ш^1$ defined in 8.6.2. The book contains many results including Grunwald-Wang on it.
Mar
6
comment Have locally principal crossed homomorphisms been studied?
You are asking about the kernel of $H^1(H,A)\to \prod_C H^1(C,A)$ where the product runs over all cyclic subgroups $C$ in $H$. In Galois cohomology these kernels appear often when studying local-to-global principles as the product can also be viewed as running also over all localisations at unramified places by Chebotarev.
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