My original question is from this ME post but I think I need a broader understanding for this. The Schwartz space $\mathcal{S}$ and its subspaces are examples of nuclear spaces. In fact, any closed subspace of the Schwartz space is a nuclear Fréchet space. Also, for any closed subspace $V$ of $\m...

Is there a version of the Bloch–Beilinson conjecture for smooth projective varieties over global fields of positive characteristic? The conjecture I’m referring to is the “recurring fantasy” on page 1 of Bloch - Algebraic cycles and values of L-functions, though I’m particularly interested in the...

This post is based on the answer to this question: A claim on partitioning a convex planar region into congruent pieces A perfect congruent partition of a planar region is a partition of it with no portion left over into some finite number n of pieces that are all mutually congruent. The answer f...

The paper Dividing a polygon into two similar polygons proves that there are only three families of polygons that are irrep-2-tiles (can be subdivided into similar copies of the original). Right angled triangles $1:\sqrt{2}$ parallelograms The Golden Bee I wish to find examples of polyhedra tha...

I encountered the following object in $\mathbb{C}^3$ defined for $m\in\mathbb{N}$ by $$A_m:=\lbrace (z_1,z_2,z_3)\in\mathbb{C}^3|(2^{2z_3}m-1)2^{2z_1+z_2+1}+3^{z_2-1}(2^{2z_1}-2^2-3^{z_3+1}m)=0\rbrace$$ for which I need to find integer points $(n_1^{(m)},n_2^{(m)},n_3^{(m)})\in A_m\cap\mathbb{N}^...

In the previous question, I find that situation is much less favorable than expected…. So I add more details to focus on the specific case I have in mind. Let us consider the Schwartz space $\mathcal{S}(\mathbb{R}^{mN})$ and denotes its elements as $f(x_1, \dotsc, x_N)$ with $x_1, \dotsc, x_N \in...

I have already asked basically the same question here, but now I have found a way to rephrase it simply, so this new formulation might be more interesting. Consider a union-closed family $\mathcal{F}$ of $n$ finite sets with $\mathcal{F} \not = \{ \emptyset \}$. Let $\mathcal{H} \subset \mathcal{...