# All Questions

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### intersection of finitely many maximal ideals

For what commutative rings with infinitely many maximal ideals we can say that the intersection of any combination of finitely many maximal ideals is not zero? Obviously it holds for Dedekind domains ...
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### Poincaré bundle and Weil pairing for Abelian schemes

In which situations is there a Poincaré bundle for Abelian schemes? In [Mumford, Abelian varieties] only the case of Abelian varieties is treated. The same question for the Weil pairing ...
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### $\mathbb{P}^1$-fibrations over $\mathbb{P}^2$ that are not rational

We know that if $X$ is a smooth complex projective variety and we assume that there is a dominant morphism $f : X \to Y$ with $Y$ and the general fibers of $f$ rationally connected. Then $X$ itself is ...
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### Normalization of a curve and push forward of vector bundles

Let $C$ be a projective curve (over an algebraically closed field, not necessarily of characteristic zero) which is smooth except for exact one node. Let $\pi:\tilde{C} \to C$ be its normalization. ...
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### p-adic valuation of a sum

Let $n_1$, ..., $n_k$ denote positive integers, and let us write $$n_i=\prod_{j=1}^m p_j^{\alpha_{ij}}$$ for $1\le i\le k$, where the $p_j$'s are distinct prime numbers, and $\alpha_{ij}\ge 0$ for ...
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### Transfinite sequence of contiguous simplicial maps

Recall that two simplicial maps of (abstract) simplicial complexes $f,g\colon K\to L$ are contiguous if $f(\sigma)\cup g(\sigma)$ is a simplex of $L$ for every simplex $\sigma\in K$. Contiguous ...
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### What are all the stationary and pointwise independent random processes?

In the 60's, I. Gel'fand introduced the concept of generalized stochastic processes (Ch. III, Vol. 4 of his work on Generalized functions). For a generalized stochastic process $\Phi$, he defines the ...
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### What is the best result of asymmetric sparse connector of depth 2 so far?

What is the best result of asymmetric sparse connector of depth 2 so far? The sparse connector problem can be represented by a digraph. Given $n, N \in \aleph \left(n\leq N \right)$, construct a ...
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### Neeman's homotopy limits in stable $\infty$-categories

Related question (I hoped to turn this into an answer for the user, but in the end it became a question on its own right!): this In the book Neeman, Amnon. Triangulated categories. No. 148. ...
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### The Borel construction of equivariant cobordism

In $K$ theory, the Borel construction of equivariant cohomology is somehow not the right one. The $G$-equivaraint $K$ theory of a point should be the representation ring of $G$, but $K(BG)$ is this ...
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### Is this a valid way to prove that this infinite sum is divergent? [migrated]

I have the infinite sum: $$\sum_{n=1}^{\infty}\frac{1}{2(n+2)}$$ In this sum I observe that all instances of n is added with 2 before used. Therefor I would think i could do this ...
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### Lim inf and lim sup for a specific sequence of sets [on hold]

Let the indicator function be defined as $$I(x) \triangleq \begin{cases} 1, & \quad x \geq 0 \\ 0, & \quad x < 0 \end{cases}$$ and $I_{\nu}(x) \in [0,1]$ be an approximation of the $I(x)$ ...
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### Does positivity preserve compactness? [on hold]

Suppose $A$ and $B$ are operators on a (separable) Hilbert space $H$ and $A \leq B$. Is it true that if $B$ is compact then $A$ is compact too? If not, could you please show a counterexample?
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### Trivial Legendrian deformations defined by infinitesimal Sasakiautomorphisms

I'm reading the paper Y. Ohnita: On deformation of 3-dimensional certain minimal Legendrian submanifolds, Proceedings of The Thirteenth International Workshop on Differential Geometry and Related ...
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### Boolean Algebra - Simplifying circuits [on hold]

Here is the question F = AB(CD + A~B + ~AD) + AD(C + ~D)‏ My attempt ABCD + ABA~B- + AB~AD + ADC + AD~D ....multiplying out the brackets = ABCD + A0 + 0BD + ADC + A0 .... X.~X = 0 = ABCD ...
### Invariant subsets of $z \mapsto z^2$
Where can I find an explicit construction of closed invariant subsets of the map $z \mapsto z^2$ on the unit circle? Furstenberg mentions that there are continuum of such disjoint minimal sets but ...