bio | website | mathematik.uni-mainz.de/… |
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location | Mainz | |
age | 26 | |
visits | member for | 4 years, 7 months |
seen | Oct 15 at 21:54 | |
stats | profile views | 2,464 |
Post-doc at Johannes-Gutenberg UniversitÃ¤t 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) |