4,812 reputation
21336
bio website iazd.uni-hannover.de/…
location Hanover, Germany
age 29
visits member for 4 years, 11 months
seen 1 hour ago

I am a postdoc at the Leibniz Universität Hannover. I specialise in arithmetic geometry, algebraic number theory and analytic number theory.


8h
asked Relative Picard functor for the Zariski topology
Mar
23
revised Twists of projective automorphisms
deleted 9 characters in body
Mar
20
comment Twists of projective automorphisms
I mean those $\sigma \in \mathrm{Aut} X$ such that $\sigma^*L \cong L$. Certainly I want $\mathrm{Aut}(\mathbb{P}^n, \mathcal{O}(1) )$ to be $\mathrm{PGL}_{n+1}$.
Mar
20
asked Twists of projective automorphisms
Mar
17
revised Obstruction and rational points on curves
added 23 characters in body
Mar
17
answered Obstruction and rational points on curves
Mar
16
comment Number of solutions of arithmetic function's equation
There is no asymptotic formula for $\omega(x)$; instead one knows that its maximal order is equal to what you claim. Anyway, one easily sees using the PNT that $2\pi(x) - \pi(2x) \sim 2 (\log 2) x/(\log x)^2$, which proves that there are only finitely many such $x$ satisfying your equation.
Mar
16
comment zeta function of abelian varieties and the exterior algebra
math.stackexchange.com/questions/137951/…
Mar
11
comment Unramified extensions of a given degree
If $K$ is a local field, then there exists a unique unramified extension of each degree. See Serre's book on local fields.
Mar
6
comment Variety acquiring rational point over any quadratic extension
For some classes of varieties one can prove that this cannot happen. For example, if a smooth cubic hypersurface over $\mathbb{Q}$ has a point over a single quadratic extension of $\mathbb{Q}$, then it already has a point over $\mathbb{Q}$.
Mar
4
comment A reference for $\mathbb{A}^1_R$ being a coarse moduli space of the stack of elliptic curves
I don't have it with me, so I'm not sure if it's in there, but have you tried looking in Katz, Mazur - Arithmetic Moduli of Elliptic Curves ?
Feb
18
comment Automorphisms of generic complete intersections
Thanks for the answer, but I think you have misunderstood the problem. I'm ultimately trying to show that $\sigma^*$ can't be the identity when $\sigma$ is non-trivial. So I have no idea how to handle this first case! The second case you mention is fine for me.
Feb
18
revised Automorphisms of generic complete intersections
deleted 1 character in body
Feb
11
comment automorphism group of a function field
Have you looked at what happens for $\mathbb{F}_2(t)$?
Feb
10
revised Automorphisms of generic complete intersections
added 2 characters in body
Feb
8
comment Automorphisms of generic complete intersections
Are you referring to the case of quartic surfaces? I have avoided these by assuming that $n \geq 3$ (my $n$ is the dimension of $X$, not the dimension of the ambient projective space).
Feb
8
asked Automorphisms of generic complete intersections
Feb
4
comment Is there a Poisson Summation formula for imprimitive Dirichlet characters?
It would help greatly if you stated which version of the Poisson summation formula for primitive characters you are referring to.
Jan
29
revised Automorphisms of ideals of $\mathbb{C}[t]$
edited tags
Jan
29
comment cohomological obstructions and rational points
There are other obstructions than the Brauer-Manin obstruction, such as the étale Brauer-Manin obstruction, which is in general a finer obstruction.