2
votes
2answers
496 views
Constraints on the Fourier transform of a constant modulus function
Considering the function $f:\mathbb{R} \to \mathbb{C}$, with $\left| f(x) \right|=1$ for all $x\in \mathbb{R}$.
Considering $g:\mathbb{R} \to \mathbb{C}$ with $\int_{-\infty}^{\inf …
3
votes
1answer
478 views
Can the algebraic closure of a complete field be complete and of infinite degree?
Yes, this is yet another "foundational" question in valuation theory.
Here's the background: it is a well known classical fact that the dimension (in the purely algebraic sense) o …
1
vote
0answers
63 views
Bound of polynomial on product space in terms of values on the diagonal
We work in the multivariate case so that $x$ stands for $(x_1,\ldots, x_n)$. Let $q(x,y)$ be a symmetric matrix representation of a homogeneous polynomial $f(x)$ of degree $d$. Exp …
1
vote
3answers
861 views
Algebraic Varieties which are also Manifolds
Any non-singular projective variety over $\mathbb{C}$ is easily seen to be a smooth manifold. Presumably the same is not true for algebraic varieties - one would not expect varieti …
1
vote
1answer
273 views
Does any iterative equation of n-th order have exactly n independent solutions?
Does any iterative equation of n-th order which does not inclute derivatives of order higher than 1 have exactly n independent solutions?
Let's designate n-th iterate of a functio …
3
votes
1answer
95 views
Is there an easy way to find the minimum dimensions of representations for these R-algebras?
I'm working with Clifford algebras, of which the first few are $C_0 = \mathbb{R}$, $C_1 = \mathbb{C}$, $C_2 = \mathbb{H}$, $C_3= \mathbb{H}^2$, $C_4 = M_{2,2}(\mathbb{H})$, $C_5= M …
2
votes
2answers
629 views
Nonnegative polynomial in two variables
What can be said about the polynomials $f\in\mathbb Q[x, y]$ which are nonnegative on $\mathbb R\times \mathbb R$?
Motivation: this may lead to progress in the question about …
7
votes
2answers
544 views
Is it possible for the repeated doubling of a non torsion point of an elliptic curve tstays bounded in the affine plane ?
Let P=(x1,y1) be a non torsion point on an elliptic curve y^2=x^3+Ax+B.
Let (xn,yn)=P^{2^n}. xn,yn are rationals with heights growing rapidly. Can {xn} {yn} stays bounded ?
2
votes
0answers
375 views
How to prove that a map is a Serre fibration?
I want to prove that the homotopy groups of some topological space $B$ of interest to me (not a CW complex) are trivial. I have a strategy of proof that consists in introducing ano …
5
votes
2answers
531 views
Examples of birational equivalence of a variety and a hypersurface
There's an algebraic geometry theorem (I.4.9 in Hartshorne) that says: any variety of dimension r (over an algebraically closed field) is birationally equivalent to a hypersurface …
9
votes
0answers
758 views
Are there analogues of Beilinson’s conjectures for motives with coefficients?
There's a body of wisdom (following Beilinson, Bloch, Deligne, ...) relating mixed Tate motives, motivic cohomology, algebraic K-theory, special values of L-functions, and polyloga …
1
vote
0answers
190 views
What is a Cheeger deformation?
I'm currently at a Differential Geometry meeting and there is a mini-course on positively curved Riemannian manifolds. There, we were told that a technique to construct such manifo …
4
votes
0answers
297 views
A relative Noether number for invariants
EDIT: Wrong definition of $\beta\left(G,H\right)$ fixed. One of the results is open (i. e., I cannot prove it).
In "Finite Groups and invariant theory" (a paper in Malliavin's L …
6
votes
1answer
509 views
Are automorphism groups of hypersurfaces reduced ?
In the following article : "H. Matsumura, P. Monsky, On the automorphisms of hypersurfaces, J. Math. Kyoto Univ. 3 (1964) 347-361", it is shown that in finite characteristic, autom …
0
votes
1answer
161 views
Does every smooth integrable constant-rank distribution have a basis in which the structure constants are traceless?
My question is local and coordinate-full: I have an open neighborhood $0 \in U \subseteq \mathbb R^n$, and I'm allowed to make it smaller around $0$. On this neighborhood, I have …
