bio | website | www2.imperial.ac.uk/~rpanneko |
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location | London, United Kingdom | |
age | ||
visits | member for | 3 years, 9 months |
seen | 8 mins ago | |
stats | profile views | 1,328 |
I am a postdoc at Imperial College. My interests are rational points on varieties, in particular K3 surfaces and abelian varieties.
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 |
Jun 8 |
comment |
Find all rational solutions of this diophantine-equation?
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 $p^2-r^2=1$ 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 diophantine-equation?
sign errors |
Jun 7 |
revised |
Find all rational solutions of this diophantine-equation?
added 9 characters in body |
Jun 7 |
revised |
Find all rational solutions of this diophantine-equation?
added 150 characters in body |
Jun 7 |
revised |
Find all rational solutions of this diophantine-equation?
checked that the branch locus consists of exactly 8 points |
Jun 7 |
revised |
Find all rational solutions of this diophantine-equation?
corrected solution |