bio | website | mathematik.uni-mainz.de/… |
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location | Mainz | |
age | 26 | |
visits | member for | 4 years, 6 months |
seen | 2 days ago | |
stats | profile views | 2,391 |
Post-doc at Johannes-Gutenberg UniversitÃ¤t 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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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? |