2,830 reputation
1837
bio website mathematik.uni-mainz.de/…
location Mainz
age 26
visits member for 4 years, 7 months
seen Oct 15 at 21:54

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


Oct
15
accepted Zograf's bound on the index of a modular curve for Shimura curves
Oct
14
asked Can the hyperbolic core of a curve over $\mathbb Q$ be defined over $\mathbb Q$ as an algebraic stack
Oct
2
revised smooth connected affine scheme over Z has good reduction almost everywhere
added 44 characters in body
Oct
1
comment smooth connected affine scheme over Z has good reduction almost everywhere
Possibly. But what about working with the sheaf of differentials. This is a coherent sheaf on the arithmetic scheme defined by your polynomial. It is generically free by your assumption (of smoothness over the field of rational numbers). Do you see that it is locally free outside a finite set of primes?
Oct
1
answered smooth connected affine scheme over Z has good reduction almost everywhere
Oct
1
comment smooth connected affine scheme over Z has good reduction almost everywhere
Not true. Take $f = y^2- x^3$. This is not smooth over the generic fibre. You need more than an irreducible polynomial. The type of statements you are looking for are sometimes coined "spreading out". See Bjorn Poonen's notes on rational points. For example, any nice morphism of schemes $X \to S$ which is generically smooth is smooth over an open of $S$. That's the statement you are looking for. (It's a consequence of the fact that the locus of smoothness is open. Thus, if your polynomial $f$ defines a smooth variety modulo some $p$, then it defines a smooth variety over $\mathbb Q$.)
Sep
30
awarded  Explainer
Sep
30
awarded  Nice Answer
Sep
29
reviewed Approve suggested edit on Connected components of the complement of a degree-d affine hypersurface
Sep
16
comment Can the Grothendieck ring of varities over a field $k$ be defined for non separated schemes?
Sorry I misread the question.
Sep
16
awarded  Popular Question
Sep
16
comment Can the Grothendieck ring of varities over a field $k$ be defined for non separated schemes?
Have a look at mathoverflow.net/questions/25122/… for instance. Of course, you can define the grothendieck group without the condition of separatedness. I think noetherian (or just locally noetherian) should be enough; see Definition 1.4 in math.leidenuniv.nl/scripties/MasterJavanpeykar.pdf (I dont recommend you read that text too thoroughly...)
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)