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bio website www2.imperial.ac.uk/~rpanneko
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I am a postdoc at Imperial College. My interests are rational points on varieties, in particular K3 surfaces and abelian varieties.


Dec
3
revised rational points of a hyperelliptic curve
added latex
Dec
3
suggested approved edit on rational points of a hyperelliptic curve
Nov
30
suggested rejected edit on p-power roots of unity in local fields
Nov
25
comment Fermat's last theorem over larger fields
I think the answer is yes, since a non-hyperelliptic genus 3 curve is a plane quartic, and every quartic polynomial (in one variable) has solvable Galois group. Nice answer/comment, by the way!
Nov
25
comment Fermat's last theorem over larger fields
Ah, of course, thanks!
Nov
25
comment Fermat's last theorem over larger fields
Just curious, what is the reason for asking about the $n=5$ case specifically? I thought about the $n=4$ case and I couldn't answer that either -- but perhaps you can?
Nov
25
comment Fermat's last theorem over larger fields
(OK, except the trivial rational solutions, that is.)
Nov
25
comment Fermat's last theorem over larger fields
I'm really curious about how you want to apply HIT here! I would think that, on the contrary, no preimage of a rational point will give a Galois point, since you're extracting a fifth root, so you're missing a primitive fifth root of unity in your residue field!
Oct
24
awarded  Disciplined
Oct
23
comment Does every smooth, projective morphism to $\mathbb{C}P^1$ admit a section?
Those are never smooth, I think?
Oct
17
comment Equidistribution of rational points on an algebraic variety
You're absolutely right. I just wanted to show the answer is "no" even if one restricts attention to those elements of $X(\mathbb{F}_q)$ that are in the image of the reduction map.
Oct
17
comment Equidistribution of rational points on an algebraic variety
Probably yes. Don't have time to think about a proof though.
Oct
17
revised Equidistribution of rational points on an algebraic variety
edited body
Oct
17
answered Equidistribution of rational points on an algebraic variety
Oct
10
comment Are there noncommutative extensions of $\alpha_p$ by $\mathbb{G}_m$?
Actually, I know of no serious source that uses that phrase to mean an extension of the form $0 \rightarrow A \rightarrow E \rightarrow B \rightarrow 0$, but I would love to be shown an example.
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. :)