1,658 reputation
818
bio website www2.imperial.ac.uk/~rpanneko
location London, United Kingdom
age
visits member for 3 years
seen 4 hours ago

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