11
votes
2answers
1k views
Should there be a true model of set theory?
As I understand it, there is a program in set theory to produce an ultimate, canonical model of set theory which, among other things, positively answers the Continuum Hypothesis an …
0
votes
0answers
169 views
Recurrence relation with Hadamard Product
I've been drawn to a problem that requires ascertaining the existence of fixed points in the following recurrence relation, any ideas would be much appreciated. I seek neccessary c …
11
votes
4answers
970 views
What is the Euler characteristic of a Hilbert scheme of points of a singular algebraic curve?
Let $X$ be a smooth surface of genus $g$ and $S^nX$ its n-symmetrical product (that is, the quotient of $X \times ... \times X$ by the symmetric group $S_n$). There is a well know …
4
votes
4answers
497 views
Examples of $G_\delta$ sets
Recall that a subset A of a metric space X is a $G_\delta$ subset if it can be written as a countable intersection of open sets. This notion is related to the Baire category theore …
9
votes
2answers
748 views
Is completeness of a field an algebraic property?
Pretty straitforward:
If a field has a metric in which it is complete can it have a metric in which it is not complete?
By metric I mean field norm of course
1
vote
3answers
437 views
Stably free module not finitely generated is free
Hi. I have read that stably free modules not finitely generated are free; this is proved in
M.R. Gabel, stably free projectives over commutative rings, Thesis, Brandeis Univ., Wal …
6
votes
2answers
402 views
Radix notation and toposes
In classical logic plus ZF, the field of real numbers admits infinitely many isomorphic realizations as a numeral system --- as the radix varies. The intuitionistic status of thes …
0
votes
2answers
507 views
Cosine of a Partial Sum
Does anyone know of a closed formula for $cos(\displaystyle\sum_{n=0}^m a_{n})$? I've seen formulas for $cos(\displaystyle\sum_{n=0}^\infty a_{n})$ and $tan(\displaystyle\sum_{n=0} …
2
votes
2answers
222 views
Hamiltonians of compatible Poisson tensors
Hi!
Given two Poisson tensors $\pi_0$ and $\pi$ (on a Lie group $G$) ; if the two tensors are compatible, i.e.
$$[\pi_0,\pi]=0$$
what are the relations between their hamiltonians …
8
votes
1answer
400 views
Functorial way of showing that the Segre (or Plucker) morphism is a closed embedding?
Let $\mathcal{F}, \mathcal{G}$ be quasi-coherent sheaves on a base scheme $S$. Then the $S$-schemes $\mathbb{P}(\mathcal{F}), \mathbb{P}(\mathcal{G})$ are defined by a universal pr …
2
votes
1answer
581 views
Is every projective space bundle locally trivial in the Zariski topology?
Suppose given a smooth morphism $f:X\to Y$ between varieties over $\mathbb{C}$ whose fibres are $\mathbb{P}^n$. Then I have an equality of Hodge polynomials
$H(X) = H(Y)H(\mathbb …
13
votes
0answers
470 views
Lipschitz Homeomorphisms Between Spheres of N-dimensional Spaces
Let $B_p^N$ be the unit ball of $\mathbb{R}^N$ under the $\ell_p^N$ norm.
Question: Let $C_N$ be the infimum of all $C$ for which there is a homeomorphism $f_N$ from $B_\infty …
7
votes
1answer
797 views
If the numerical equivalence of cycles coincides with the homological one, does the Hodge standard conjecture follow?
Suppose that over an algebraically closed field $K$ of finite characteristic the numerical equivalence of cycles relation (for algebraic cycles of smooth projective varieties) coin …
6
votes
1answer
499 views
pontryagin dual of the group S^{-1}Z
$T$ is a set of some prime numbers. $S$ is the multiplictive set generated by $T$.
How to compute the Pontryagin dual of $S^{-1}Z$ ($Z$ is integal ring and $S^{-1}Z$ is localizatio …
13
votes
3answers
601 views
Non-vanishing cohomology of line bundles on projective varieties in prime characteristic?
This is a somewhat naive question about the expected non-vanishing behavior of sheaf cohomology groups $H^i(X, \mathcal{L})$, where $X$ is a smooth projective variety of dimension …
