1,621 reputation
618
bio website www2.imperial.ac.uk/~rpanneko
location London, United Kingdom
age
visits member for 2 years, 10 months
seen 11 hours ago

I am a postdoc at Imperial College. My interests are rational points on varieties, in particular K3 surfaces and abelian varieties.


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.”?
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May
27
answered Is there an english translation of Delignes “La conjecture de Weil pour les surfaces K3.”?
May
20
comment Do all exact sequences $0 \rightarrow A \rightarrow A \oplus B \rightarrow B \rightarrow 0$ split for finitely generated abelian groups?
It isn't stated what the maps are, so it is not clear that that would give a splitting.
May
16
revised Quadratic twist of curve defined over finite field
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May
16
comment Quadratic twist of curve defined over finite field
Oh, you're absolutely right. Thanks!
May
16
revised Quadratic twist of curve defined over finite field
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May
15
revised Quadratic twist of curve defined over finite field
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May
15
answered Quadratic twist of curve defined over finite field
May
9
revised Why are torsion points dense in an abelian variety?
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May
9
suggested suggested edit on Why are torsion points dense in an abelian variety?
May
6
awarded  Excavator