Newest Questions
166,651 questions
34
votes
6
answers
11k
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What is the universal property of normalization?
What is the universal property of normalization? I'm looking for an answer something like
If X is a scheme and Y→X is its
normalization, then the morphism
Y→X has property P and any ...
- 24.9k
7
votes
3
answers
669
views
Weil divisors on non Noetherian schemes
Let X be an integral scheme that is separated (say over an affine scheme). Define a Weil divisor as a finite integral combination of height 1 points of X, where the height of a point of X is the ...
- 4,008
98
votes
8
answers
107k
views
Which are the best mathematics journals, and what are the differences between them? [closed]
Suppose you have a draft paper that you think is pretty good, and people tell you that you should submit it to a top journal. How do you work out where to send it to?
Coming up with a shortlist isn't ...
9
votes
3
answers
2k
views
If $\Omega_{X/Y}$ is locally free of rank $\mathrm{dim}\left(X\right)-\mathrm{dim}\left(Y\right)$, is $X\rightarrow Y$ smooth?
Suppose I have a morphism $f:X\rightarrow Y$ such that the relative sheaf of differentials $\Omega_{X/Y}$ is locally free. Does it follow that $f$ is smooth?
The answer is no, but for a silly reason. ...
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19
votes
2
answers
2k
views
Homomorphism more than 3/4 the inverse
Suppose $G$ is a finite group and $f$ is an automorphism of $G$. If $f(x)=x^{-1}$ for more than $\frac{3}{4}$ of the elements of $G$, does it follow that $f(x)=x^{-1}$ for all $x$ in $G\ ?$
I know ...
- 5,395
13
votes
2
answers
3k
views
Non-quasi separated morphisms
What are some examples of morphisms of schemes which are not quasi separated?
- 621
3
votes
1
answer
459
views
Are there any criteria for a presheaf which is an etale sheaf to be a sheaf in the fppf topology?
I am happy to hear answers to variants too. For instance, my situation I actually have a sheaf in the smooth topology.
- 10.9k
20
votes
22
answers
5k
views
LaTeX based document editors
I'm afraid my first question isn't a math puzzle per se, but rather question of math "presentation" . Basically I've been out of school for a year or two - so I'm a bit out of practice in writing up ...
3
votes
2
answers
998
views
Is there an example of an algebraic stack whose closed points have affine stabilizers but whose diagonal is not affine?
Burt Totaro has a result that for a certain class of algebraic stacks, having affine diagonal is equivalent to the stabilizers at closed points begin affine. Is there an example of this equivalence ...
- 10.9k
63
votes
9
answers
24k
views
Can a vector space over an infinite field be a finite union of proper subspaces?
Can a (possibly infinite-dimensional) vector space ever be a finite union of proper subspaces?
If the ground field is finite, then any finite-dimensional vector space is finite as a set, so there are ...
- 24.9k
9
votes
1
answer
755
views
Is there a good version of Artin-Wedderburn for semisimple algebra objects?
Artin-Wederburn says that if you have a semisimple algebra then it is a product of matrix algebras over division rings.
Suppose that $C$ is a fusion category over the complex numbers (if you want to ...
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53
votes
5
answers
6k
views
Can $N^2$ have only digits 0 and 1, other than $N=10^k$?
Pablo Solis asked this at a recent 20 questions seminar at Berkeley. Is there a positive integer $N$, not of the form $10^k$, such that the digits of $N^2$ are all 0's and 1's?
It seems very unlikely,...
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43
votes
4
answers
13k
views
Finite extension of fields with no primitive element
What is an example of a finite field extension which is not generated by a single element?
Background: A finite field extension E of F is generated by a primitive element if and only if there are a ...
- 24.9k
39
votes
18
answers
26k
views
Learning about Lie groups
Can someone suggest a good book for teaching myself about Lie groups? I study algebraic geometry and commutative algebra, and I like lots of examples. Thanks.
25
votes
6
answers
6k
views
Is a quotient of a reductive group reductive?
Is a quotient of a reductive group reductive?
Edit [Pete L. Clark]: As Minhyong Kim points out below, a more precise statement of the question is:
Is the quotient of a reductive linear group by a ...
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