bio | website | iazd.uni-hannover.de/… |
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location | Hanover, Germany | |
age | 30 | |
visits | member for | 5 years, 3 months |
seen | 7 hours ago | |
stats | profile views | 2,545 |
I am a postdoc at the Leibniz UniversitÃ¤t Hannover. I specialise in arithmetic geometry, algebraic number theory and analytic number theory.
Jun 26 |
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What is known about order of torsion of jacobian of hyperelliptic curve over finite field?
Every element of $J(\mathbb{F}_p)$ is torsion, as the group is finite. As for bounds, google for the Weil conjectures. |
Jun 26 |
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References for modular curves over finite fields
I'm voting to close this question as off-topic because this was answered on math.stackexchange. |
Jun 25 |
accepted | Specialisation of rigid varieties |
Jun 25 |
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Specialisation of rigid varieties
Ok. If you know of any counter-examples in the Fano case, I would be most interested. |
Jun 25 |
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Specialisation of rigid varieties
Is the Mukai-Umemura threefold really rigid? I thought that prime Fano threefolds of genus 12 had positive dimensional moduli. |
Jun 25 |
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Specialisation of rigid varieties
Hi Jason. Thanks for the answer! Your examples seem to suggest that things are a lot better behaved in the Fano case. Do you know of any counter-examples to my question if I moreover assume that the special fibre and generic fibre are both Fano? |
Jun 25 |
asked | Specialisation of rigid varieties |
Jun 20 |
answered | meaning of $k$-rational for closed subschemes |
Jun 17 |
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Number of solutions in a sum of squares Diophantine equation
I'm voting to close this question as off-topic because it has been answered. |
Jun 15 |
accepted | Non-algebraic K3 surfaces in characteristic $p$ |
Jun 15 |
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Non-algebraic K3 surfaces in characteristic $p$
Quite possibly; does every non-algebraic K3 surface over $\mathbb{C}$ arise this way? |
Jun 15 |
asked | Non-algebraic K3 surfaces in characteristic $p$ |
Jun 8 |
accepted | Picard groups of Fano varieties in positive characteristic |
Jun 4 |
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Picard groups of Fano varieties in positive characteristic
@Jason: I don't quite follow, what is the problem with small $\ell$? Is the issue with possible $\ell^\infty$-torsion in the Brauer group? Won't this problem "go away" as we are taking a projective limit over all $\mathrm{Br}[\ell^n]$? |
Jun 3 |
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Picard groups of Fano varieties in positive characteristic
Thanks for the answer Jason. I will have a think about the argument you give. Do you know a precise reference where finiteness of the Brauer group of rationally connected varieties is proved? |
Jun 3 |
asked | Picard groups of Fano varieties in positive characteristic |
Jun 1 |
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Isotropic ternary forms
Use stereographic projection. |
May 31 |
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Are there infinitely many N^3 (especially for prime N) that cannot be expressed as a sum of three positive cubes?
Also, as you no doubt know, determining which integers are a sum of three (possibly negative) cubes is a very difficult open problem (see e.g. mathoverflow.net/questions/138886/…). One would think that your problem were easier as you are working with a cube, but restricting to positive cubes seems to complicate things. |
May 31 |
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Are there infinitely many N^3 (especially for prime N) that cannot be expressed as a sum of three positive cubes?
This problem seems quite difficult. The issue, of course, is that there are no local obstructions in this case: there are always solutions in all $\mathbb{Z}_p$ and $\mathbb{R}$. So you would need to try to use a finer obstruction, e.g. a Brauer-Manin obstruction. |
May 27 |
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Obstruction to get a galois invariant cycle
Actually the Tate conjecture only applies with rational coefficients whereas here you are working with integral coefficients, so it perhaps not so clear whether the Tate conjecture can be used. |