bio | website | www2.imperial.ac.uk/~rpanneko |
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location | London, United Kingdom | |
age | ||
visits | member for | 2 years, 10 months |
seen | 11 hours ago | |
stats | profile views | 973 |
I am a postdoc at Imperial College. My interests are rational points on varieties, in particular K3 surfaces and abelian varieties.
Jul 7 |
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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 |
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Minimal fields of isomorphism for varieties
(I was considering $K=\mathbb{Q}$ here, by the way.) |
Jul 7 |
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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 |
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Minimal fields of isomorphism for varieties
Pull-back along what then? The covering map has degree $d^2$. |
Jul 2 |
awarded | Curious |
Jun 23 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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Quadratic twist of curve defined over finite field
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May 16 |
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Quadratic twist of curve defined over finite field
Oh, you're absolutely right. Thanks! |
May 16 |
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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 |
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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 |