# All Questions

100,865 questions
522 views

### Naive Z/2-spectrum structure on E smash E?

Let $E$ be a spectrum. Then $E \wedge E$ is a $\mathbb{Z}/2$-spectrum in the naivest possible sense, i.e., an object with $\mathbb{Z}/2$-action in the (∞,1)-category of spectra. Can I make it ...
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### finite surjective l.c.i morphism is flat

Let $X,Y$ be locally Noetherian schemes. Let $f:X\to Y$ be a finite, surjective, and locally complete intersection morphism, i.e., locally it can be decomposed as regular immersion followed by a ...
536 views

### When is a commutative ring the limit of its local rings?

Let $A$ be a commutative ring. Then we get local rings $A_p$ by localizing at each prime ideal $p$. Moreover, we get $A_p \rightarrow A_q$ when $p$ contains $q$. So we get a big diagram indexed by the ...
533 views

### Some examples of depth

This is related to the question I asked last time. This sounds a bit too specific, I hope this question is still acceptable on MO. I am still not quite comfortable with the concept of depth, and ...
846 views

### Extremal question on matrices

The following question was posed to me a while ago. No one I know has a given a satisfactory (or even a complete) proof: Suppose that $M$ is an $n$ x $n$ matrix of non-negative integers. Additionally,...
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### Springer corresponding for nullcones other than the standard nilpotent cone

I understand the ordinary Springer correspondence gives a bijection between orbits in the nilpotent cone for the adjoint representation and irreducible representations of the Weyl group, through ...
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### Two conjectures by Gabber on Brauer and Picard groups

In a paper I need to make reference to 2 conjectures by Gabber (see Conjectures 2 and 3, page 1975) http://www.mfo.de/programme/schedule/2004/32/OWR_2004_37.pdf 1) Let $R$ be a strictly henselian ...
290 views

### Paritioning a set of numbers A into two sets B,C so that abs(prod(B) - prod(C)) is minimal

Let A = $\{a_1,...,a_n\}$ be a set of numbers. We can assume all elements of A are integers. Is there any efficient way to partition A into two sets B = $\{b_1,...,b_k\}$ and C = $\{c_1,...,c_l\}$ ...
1k views

### Inversion of Laurent series

For a power series $f(z) = \sum_{i=0}^{\infty} a_i z^i$ with $a_1$ nonzero, Lagrange's inversion formula gives an explicit way to compute the Taylor coefficients of the inverse function. Is there any ...
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961 views

### Is Dependent Choice all we really need?

http://en.wikipedia.org/wiki/Axiom_of_dependent_choice Is DC sufficient for the understanding of objects that are countable in some suitable sense? For example, is DC sufficient for the full ...
230 views

### morphisms from abelian varieties to rational curves.

Let $A$ be an abelian variety and and $\sigma$ an automorphism of $A$. Suppose $f:A\rightarrow P^1$ is a morphism. Is it true that $\sigma$ descends to an automorphism of $P^1$? I seem to remember ...
32k views

### Which math paper maximizes the ratio (importance)/(length)?

My vote would be Milnor's 7-page paper "On manifolds homeomorphic to the 7-sphere", in Vol. 64 of Annals of Math. For those who have not read it, he explicitly constructs smooth 7-manifolds which are ...
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### Math journal for high school students?

I recently discovered The College Mathematics Journal and enjoyed reading through some of the articles on fun applications of mathematics. I'd like to send some of the articles to my younger sister, a ...
903 views

### Interpolation of sequences by analytic functions

Given a sequence of complex numbers $a_n$ with $n\in\mathbb{N}$, is it possible to find an analytic (or meromorphic) function that interpolates this sequence in the sense that $f(n)=a_n$? If this is ...
1k views

### When is an Albanese variety principally polarized?

Let (X,x) be a pointed projective variety. Then there exists an abelian variety V which is universal for maps of pointed varieties $(X,x) \to (A,e_A)$, called the albanese variety. When X is a curve, ...
329 views

### A graph connectivity problem (restated)

Given an undirected connected graph, our goal is to remove some edges to make the graph disconnected. The constraint is that each node of the graph can not lose more than $m$ edges incident to it. I ...
$\newcommand{\bb}{\mathbb}\DeclareMathOperator{\gal}{Gal}$ Before stating my question I should remark that I know almost nothing about etale cohomology - all that I know, I've gleaned from hearing off ...