bio  website  www2.imperial.ac.uk/~rpanneko 

location  London, United Kingdom  
age  
visits  member for  3 years, 10 months 
seen  11 hours ago  
stats  profile views  1,337 
I am a postdoc at Imperial College. My interests are rational points on varieties, in particular K3 surfaces and abelian varieties.
1d

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 unitizationprocess of unital and nonunital $C^*$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 
Jun 8 
comment 
Find all rational solutions of this diophantineequation?
But I didn't use that polynomial to determine the rational solutions, I used it to get the genus of $C$, and so deduce finiteness of the solution set. (In fact, the zeros of the polynomial don't give rational solutions at all, since then by $p^2r^2=1$ the corresponding $r$values would have to have degree $\leq 2$ over $\mathbb{Q}$, whereas I found that they have degree $4$...) 
Jun 8 
awarded  Enlightened 
Jun 8 
awarded  Nice Answer 
Jun 8 
revised 
Find all rational solutions of this diophantineequation?
sign errors 
Jun 7 
revised 
Find all rational solutions of this diophantineequation?
added 9 characters in body 