bio | website | www2.imperial.ac.uk/~rpanneko |
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location | London, United Kingdom | |
age | ||
visits | member for | 3 years |
seen | 4 hours ago | |
stats | profile views | 998 |
I am a postdoc at Imperial College. My interests are rational points on varieties, in particular K3 surfaces and abelian varieties.
Sep 18 |
awarded | Yearling |
Sep 14 |
comment |
Is there such thing as the Gorensteinification of a one-dimensional local ring?
+1 for "Gorensteinification". |
Sep 10 |
comment |
Squarefree numbers with all digits equal 1
When $p=3$ the condition $9 \mid k$ is necessary and sufficient. So I guess the real question is whether there are infinitely many squarefree numbers of this form, given how many are definitely not squarefree. |
Sep 10 |
answered | Hasse principle and twists of $\mathbb{P}^n$ |
Aug 25 |
comment |
Rational points techniques on curves not using their Jacobian
I am wondering whether $J(\mathbb{Q})$ can indeed be dense in $J(\mathbb{Q}_p)$ for all $p$, as you say is true for your $C$. I actually think this can't ever happen, using an argument very much analogous to the one presented in this question: mathoverflow.net/questions/113968/… (to which you supplied the winning answer, incidentally). I am of course also curious what your $C$ is, if you'd care to disclose such information. :) |
Aug 8 |
awarded | Necromancer |
Jul 31 |
revised |
If an abelian category $\mathcal{A}$ has enough injectives then so does $\mathrm{Ch}^{\geq 0}(\mathcal{A})$
added algebraic topology tag |
Jul 31 |
suggested | suggested edit on If an abelian category $\mathcal{A}$ has enough injectives then so does $\mathrm{Ch}^{\geq 0}(\mathcal{A})$ |
Jul 27 |
revised |
How do I show that a separable isogeny is central?
converted the occurrences of 'ker' from italic to normal text |
Jul 27 |
suggested | suggested edit on How do I show that a separable isogeny is central? |
Jul 7 |
comment |
Minimal fields of isomorphism for varieties
I completely agree with that. Note however that "period divides index" is proved exactly by your observation, namely that multiplication by $[F:K]$ factors through restriction from $K$ to $F$. |
Jul 7 |
comment |
Minimal fields of isomorphism for varieties
(I was considering $K=\mathbb{Q}$ here, by the way.) |
Jul 7 |
comment |
Minimal fields of isomorphism for varieties
@user52824: it is well-known that $H^1(K,E)$ has elements of arbitrarily high order $d$. Such an element $\alpha$ can be lifted to $H^1(K,E[d])$, which parametrizes $d$-coverings up to isomorphism (this follows from the fact that the automorphism group over $\overline{K}$ of the diagram $E \stackrel{[d]}{\rightarrow} E$ is $E[d]$ as Galois modules). If $X \rightarrow E$ is the associated $d$-covering then by "period divides index" any divisor on $X$ has degree divisible by $d$. I think Daniel claims that the index is "generically" equal to $d^2$, but I can't make this statement more rigorous. |
Jul 7 |
comment |
Minimal fields of isomorphism for varieties
Pull-back along what then? The covering map has degree $d^2$. |
Jul 2 |
awarded | Curious |
Jun 23 |
comment |
Descent of functions along finite birational morphisms
Wow, that is surprising. I was also under the impression that the answer would be 'yes', having once established this in some examples where $A$ was a non-integrally closed order in the ring of integers $B$ of a number field. So now I wonder if there is a characterization of $A\rightarrow B$ for which the aforementioned complex is exact. |
Jun 14 |
comment |
Why are polynomials so useful in mathematics?
I am surprised about the number of upvotes this question is garnering. One might as well ask why minor chords are so ubiquitous in music, or how come the word 'and' is used so often in modern literature. |
May 29 |
comment |
Torsion group of the following elliptic curve
A full proof can also be found here: www2.imperial.ac.uk/~rpanneko/m4p32/exercises4sols.pdf |
May 27 |
comment |
Is there an english translation of Delignes “La conjecture de Weil pour les surfaces K3.”?
It's a good thing the answer was yes. In general proving non-existence of translations is much harder. |
May 27 |
revised |
Is there an english translation of Delignes “La conjecture de Weil pour les surfaces K3.”?
added 12 characters in body |