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1834
bio website mathematik.uni-mainz.de/…
location Mainz
age 26
visits member for 4 years, 6 months
seen 2 days ago

Post-doc at Johannes-Gutenberg Universität Mainz. Interested in many things, but especially arithmetic geometry.


Aug
25
comment Rational points techniques on curves not using their Jacobian
@DamianRössler Yes, you are right. Note that there are some other papers on his website in which he and others apply these methods to other curves. I didn't realize the OP was asking for effective techniques and probably only read his "I want to know if there are also techniques for studying $C(K)$ that don't use the Jacobian". (Quite interestingly: somethin special to Kim's approach is that it shows that these classical finiteness statements (proven by Siegel) are related to other conjectures like the Fontaine-Mazur conjecture.)
Aug
25
answered Rational points techniques on curves not using their Jacobian
Aug
25
comment Which of the Mochizuki's works are the most closely related to elliptic curves?
You could try looking at kurims.kyoto-u.ac.jp/~motizuki/…
Aug
15
comment Tate-Shafarevich groups over finitely generated fields
I see, thanks for the quick reply. Why does it not matter whether you take the sum over only the codim'n 1 points instead of all closed points?
Aug
15
comment Tate-Shafarevich groups over finitely generated fields
What did you prove exactly in your thesis? The finiteness of this set? (Note that in the question $K$ is of characteristic zero.)
Jul
30
comment Conjugate surfaces: informations about the orbits
@DanielLoughran Your guess is correct. See Criterion 1, page 3, of Gonzalez-Diez`s paper citeseerx.ist.psu.edu/viewdoc/… .
Jul
30
comment When are isotrivial families split by a finite base-change?
You are welcome.
Jul
28
revised When are isotrivial families split by a finite base-change?
improved the comments (hopefully)
Jul
26
revised When are isotrivial families split by a finite base-change?
added 95 characters in body
Jul
26
answered When are isotrivial families split by a finite base-change?
Jul
26
reviewed Approve suggested edit on Is there a non-Gorenstein ring but local Gorenstein?
Jul
16
comment Neron model: can number of components decrease after based change?
Minor nitpick: if you base-change the Neron model, then (obviously) the number of components can not decrease. What you are really asking is whether, for $X$ an abelian variety over $K$ (the function field of $R$, say) and $L/K$ finite field extension, the number of connected components of the Neron model of $X_L$ can be smaller than the number of connected components of the Neron model of $X$. As Kestutis Cesnavicius points out, this can happen unless you have semi-abelian reduction (as in the last part of your question).
Jul
6
awarded  Nice Question
Jul
2
awarded  Inquisitive
Jul
2
awarded  Curious
Jun
10
comment kernel of isogeny becomes constant after base change
I would like to recommend the book of Bosch-Lutkebohmert-Raynaud on Neron models. Especially Chapter 7.
Jun
4
comment Is there an algorithm to decide whether or not two algebraic surfaces are birationally equivalent?
...This is where you will have to use some invariant theory probably. Then, you check whether these points are in the same orbit; here you really need the full force of invariant theory. You can probably do something similar with surfaces of general type (not necessarily canonically polarized).
Jun
4
comment Is there an algorithm to decide whether or not two algebraic surfaces are birationally equivalent?
If you have two canonically polarized surfaces with the same Hilbert polynomial, you can "check" whether they are geometrically isomorphic by using invariant theory, I think. First, you consider them as points on the same Hilbert scheme (with coordinates inside some Grassmannian). Then, basically, you write down "equations" for the action of the group PGL$_n$ (some appropriate $n$)...
Jun
3
answered Is the total space of a family of normal varieties a normal variety?
Jun
2
comment Families of Fano varieties over non-hyperbolic curves
@Sasha So this gives a smooth projective non-isotrivial family of Fano sixfolds over $\mathbb P^1$ , right?