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bio website www2.imperial.ac.uk/~rpanneko
location London, United Kingdom
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visits member for 3 years, 11 months
seen 2 hours ago

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


2d
revised Does the Bombieri-Lang conjecture imply severe restrictions on rational points on twists of hyperelliptic curves?
fixed spelling
Aug
26
reviewed Approve Precise interpretability strength of $\mathcal P_{DF}(\omega)$ and $L_{\omega_1^{CK}}$
Aug
23
reviewed Approve Catalan numbers as sums of squares of numbers in the rows of the Catalan triangle - is there a combinatorial explanation?
Aug
18
reviewed Approve Integrating Powers without much Calculus
Aug
2
comment Do good math jokes exist?
It's not the student's fault. The lecturer should have mentioned the scope of the assignment!
Jul
26
reviewed Approve Degree of commutativity of finite groups and subgroups
Jul
21
reviewed Approve Where to learn about parabolic Hölder spaces and when to use them
Jul
3
reviewed Approve Goldbach's problem in algebraic number fields
Jun
27
comment Definition field of isogeny between abelian varieties
You're right that I shouldn't have written "parametrized". I have now hopefully made the text less misleading. Thanks!
Jun
27
revised Definition field of isogeny between abelian varieties
clarified
Jun
27
comment Definition field of isogeny between abelian varieties
My argument does not need that descent is effective. I just need that the set of isomorphism classes of twists in the isogeny category injects into $\operatorname{H}^1$, which is completely formal. In the present case at least, under the assumption on the geometric endomorphism ring, descent actually is effective, since the $\operatorname{H}^1$ does not change when passing from the actual category of abelian varieties, where descent is of course known to hold, to the isogeny category.
Jun
26
revised Definition field of isogeny between abelian varieties
added 27 characters in body
Jun
26
comment Definition field of isogeny between abelian varieties
Incidentally, the same argument shows that $A$ is isogenous (over $K$) to the quadratic twist $B^t$ of $B$ (which in turn implies the desired conclusion).
Jun
26
answered Definition field of isogeny between abelian varieties
Jun
25
revised How to prove that this equation has only one solution?
added tex
Jun
24
reviewed Approve Geometric meaning of a trigonometric identity
Jun
24
reviewed Approve unitization-process of unital- and non-unital $C^*$-algebras
Jun
19
comment meaning of $k$-rational for closed subschemes
I do not think there is such a notion (at least not one which is in more or less common use). But one can generalize the concept of rational point in various ways, for example one could define rational subvarieties of $X$ as geometrically integral subschemes $Z$ of $X$ (in which case a rational subvariety of dimension $0$ of $X$ is indeed a rational point on $X$). Of what use this definition would be is of course another question...
Jun
8
revised Embedding linear algebraic groups of a given dimension into a fixed $\mathrm{GL}_N$
corrected title, added tag
Jun
8
reviewed Approve Power series with matrix coefficients