1,251 reputation
311
bio website
location
age
visits member for 2 years, 4 months
seen Feb 7 '13 at 18:18

Dec
20
asked Abelian subvarieties of a principally polarized abelian variety are principally polarized
Dec
6
answered Shrinking the base field of a scheme of finite type over a field
Dec
3
comment Are there infinitely many rational functions of bounded degree and given ramification
@QiL No. I want to fix $X$. Then I want to find an integer $n$ and a finite set of points $R$ such that there are infinitely many $X\to \mathbf P^1(\mathbf C)$ of degree at most $n$ and with ramification inside $R$. For instance, if $g>1$, then $n=2$ won't work. (There is a unique hyperelliptic map $X\to \mathbf{P}^1$ if it exists at all.) You'll need to take $n$ "big enough" and $R$ also "big enough". (If I take $R$ small there aren't any $X\to \mathbf{P}^1(\mathbf{C})$ with ram locus inside $R$.)
Dec
2
comment Are there infinitely many rational functions of bounded degree and given ramification
I've edited the question. I admit the question was poorly written. Thanks for the comments. I hope it's more clear now.
Dec
2
revised Are there infinitely many rational functions of bounded degree and given ramification
Rewrote the question to make it more accessible
Dec
2
comment Are there infinitely many rational functions of bounded degree and given ramification
I just edited the question. I forgot to put the important condition that the rational function $X\to \mathbf{P}^1(\mathbf C)$ is ramified only inside $R$.
Dec
2
revised Are there infinitely many rational functions of bounded degree and given ramification
added 46 characters in body
Dec
2
asked Are there infinitely many rational functions of bounded degree and given ramification
Dec
2
comment Set of points where ring of germs is reduced is open
This usually boils down to showing the following. Let $A$ be a local noetherian ring. Then, $A$ is reduced if and only if $A_p$ is reduced for all prime ideals $p$.
Nov
30
comment Is a morphism of schemes which is proper at every fiber proper?
Any open immersion $f:X\to Y$ of schemes which isn't closed will do, right?
Nov
27
comment Are there infinitely many pairs of rational numbers such that…
I like this answer a lot. It prompts the following question: Are there infinitely many square-free integers $n$ such that $nr^2=a^3+1$ has positive rank and $ns^2=b^3+2$ has positive rank?
Nov
27
comment Closed morphism between schemes of finite type over a field induces a closed map between varieties?
Thank you QiL! I only just read your comment.
Nov
27
comment Are there infinitely many pairs of rational numbers such that…
Question: Do I understand correctly that we always have $\mathbf{Q}(\sqrt{a^3+1}) =\mathbf{Q}(\sqrt{7}) = \mathbf{Q}(\sqrt{b^3+2})$ if $(a,r)$ and $(b,s)$ lie on the curve?
Nov
26
answered Closed morphism between schemes of finite type over a field induces a closed map between varieties?
Nov
25
revised When does a ring have a flat noetherian extension?
deleted 45 characters in body
Nov
24
comment The canonical divisor of the projective line
Just to elaborate: with these charts we see that $-2 [\infty]$ is indeed a canonical divisor on $X$.
Nov
24
accepted The canonical divisor of the projective line
Nov
24
asked Can one determine in finite time whether a point is $S$-integral
Nov
24
asked The canonical divisor of the projective line
Nov
17
accepted Why do number rings have no endomorphisms